Hvac system with sustainability and emissions controls

ABSTRACT

A controller for heating, ventilation, or air conditioning (HVAC) equipment that is operable to affect an environmental condition of a building is configured to obtain predictive models that predict values of a carbon emissions control objective and another control objective as a function of control decision variables for the HVAC equipment. The controller executes an optimization process using the predictive models to produce sets of optimization results corresponding to different values of the control decision variables, the carbon emissions control objective, and the other control objective. The controller selects from the sets of optimization results based on the values of the carbon emissions control objective and the other control objective. The controller operates the HVAC equipment to affect the environmental condition of the building in accordance with the values of the control decision variables corresponding to a selected set of the optimization results.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation-in-part of U.S. application Ser. No.17/403,669, filed Aug. 16, 2021, which is a continuation-in-part of U.S.application Ser. No. 16/927,759 filed Jul. 13, 2020, which claims thebenefit of and priority to U.S. Provisional Patent Application No.62/873,631 filed Jul. 12, 2019, and U.S. Provisional Patent ApplicationNo. 63/044,906 filed Jun. 26, 2020. U.S. application Ser. No. 17/403,669is also a continuation-in-part of U.S. patent application Ser. No.17/393,138 filed Aug. 3, 2021, which is a continuation of U.S. patentapplication Ser. No. 16/927,766 filed Jul. 13, 2020, which claims thebenefit of and priority to U.S. Provisional Patent Application No.62/873,631 filed Jul. 12, 2019, and U.S. Provisional Patent ApplicationNo. 63/044,906 filed Jun. 26, 2020. This application also claims thebenefit of and priority to U.S. Provisional Application No 63/194,771,filed May 28, 2021, and U.S. Provisional Application No. 63/220,878,filed Jul. 12, 2021. The entire disclosures of all of these patentapplications are incorporated by reference herein.

BACKGROUND

The present disclosure relates generally to a building system in abuilding. The present disclosure relates more particularly tomaintaining occupant comfort in a building through environmentalcontrol.

Maintaining occupant comfort and disinfection in a building requiresbuilding equipment (e.g., HVAC equipment) to be operated to changeenvironmental conditions in the building. In some systems, occupants arerequired to make any desired changes to the environmental conditionsthemselves if they are not comfortable. When operating buildingequipment to change specific environmental conditions, otherenvironmental conditions may be affected as a result. Maintainingoccupant comfort and disinfection can be expensive if not performedcorrectly. Thus, systems and methods are needed to maintain occupantcomfort and provide sufficient disinfection for multiple environmentalconditions while reducing expenses related to maintaining occupantcomfort and disinfection.

SUMMARY

One implementation of the present disclosure is a controller forheating, ventilation, or air conditioning (HVAC) equipment, according tosome embodiments. In some embodiments, the HVAC equipment is operable toaffect an environmental condition of a building. In some embodiments,the controller includes one or more processors and memory storinginstructions that, when executed by the one or more processors, causethe one or more processors to perform operations. In some embodiments,the operations include obtaining one or more predictive modelsconfigured to predict values of a carbon emissions control objective andanother control objective as a function of control decision variablesfor the HVAC equipment. In some embodiments, the operations includeexecuting an optimization process using the one or more predictivemodels to produce multiple sets of optimization results corresponding todifferent values of the control decision variables, the carbon emissionscontrol objective, and the other control objective. In some embodiments,the operations include selecting one or more of the sets of optimizationresults based on the values of the carbon emissions control objectiveand the other control objective. In some embodiments, the operationsinclude operating the HVAC equipment to affect the environmentalcondition of the building in accordance with the values of the controldecision variables corresponding to a selected set of the optimizationresults.

In some embodiments, the carbon emissions control objective includes anamount of carbon emissions predicted to result from operating the HVACequipment in accordance with the control decision variables. In someembodiments, the other control objective includes an infection riskpredicted to result from operating the HVAC equipment in accordance withthe control decision variables.

In some embodiments, the other control objective includes at least oneof an operating cost predicted to result from operating the HVACequipment in accordance with the control decision variables or a capitalcost of purchasing or installing the HVAC equipment. In someembodiments, executing the optimization process includes executingmultiple optimization processes using different sets of constraints forthe control decision variables or different search spaces for thecontrol decision variables, the multiple optimization processesproducing corresponding sets of the multiple sets of optimizationresults.

In some embodiments, selecting one or more of the sets of optimizationresults include selecting one or more of the sets of optimizationresults for which the values of the carbon emissions control objectiveand the other control objective are not both improved by another of thesets of optimization results. In some embodiments, selecting one or moreof the sets of optimization results includes classifying the multiplesets of optimization results as either Pareto-optimal optimizationresults or non-Pareto-optimal optimization results with respect to thecarbon emissions control objective and the other control objective, andselecting the Pareto-optimal optimization results.

In some embodiments, selecting one or more of the sets of optimizationresults includes selecting a first set of optimization results thatprioritizes the carbon emissions control objective over the othercontrol objective, a second set of optimization results that prioritizesthe other control objective over the carbon emissions control objective,and a third set of optimization results that balances the carbonemissions control objective and the other control objective.

In some embodiments, the operations further include presenting thevalues of the carbon emissions control objective and the other controlobjective associated with the first set of optimization results, thesecond set of optimization results, and the third set of optimizationresults as selectable options via a user interface. In some embodiments,the operations further include determining the selected set of theoptimization results responsive to a user selecting one of theselectable options via the user interface.

Another implementation of the present disclosure is a controller forheating, ventilation, or air conditioning (HVAC) equipment, according tosome embodiments. In some embodiments, the HVAC equipment is operable toaffect an environmental condition of a building. In some embodiments,the controller includes one or more processors, and memory storinginstructions that, when executed by the one or more processors, causethe one or more processors to perform operations. In some embodiments,the operations include obtaining one or more predictive modelsconfigured to predict values of a sustainability control objective andanother control objective as a function of control decision variablesfor the HVAC equipment. In some embodiments, the operations includeexecuting an optimization process using the one or more predictivemodels to produce multiple sets of optimization results corresponding todifferent values of the control decision variables, the sustainabilitycontrol objective, and the other control objective. In some embodiments,the operations include selecting one or more of the sets of optimizationresults for which the values of the sustainability control objective andthe other control objective are not both improved by another of the setsof optimization results. In some embodiments, the operations includeoperating the HVAC equipment to affect the environmental condition ofthe building in accordance with the values of the control decisionvariables corresponding to a selected set of the optimization results.

In some embodiments, the sustainability control objective includes anamount of carbon emissions predicted to result from operating the HVACequipment in accordance with the control decision variables. In someembodiments, the other control objective includes an infection riskpredicted to result from operating the HVAC equipment in accordance withthe control decision variables.

In some embodiments, the other control objective includes at least oneof an operating cost predicted to result from operating the HVACequipment in accordance with the control decision variables or a capitalcost of purchasing or installing the HVAC equipment. In someembodiments, executing the optimization process includes executingmultiple optimization processes using different sets of constraints forthe control decision variables or different search spaces for thecontrol decision variables, the multiple optimization processesproducing corresponding sets of the multiple sets of optimizationresults.

In some embodiments, selecting one or more of the sets of optimizationresults includes classifying the multiple sets of optimization resultsas either Pareto-optimal optimization results or non-Pareto-optimaloptimization results with respect to the sustainability controlobjective and the other control objective, and selecting thePareto-optimal optimization results. In some embodiments, selecting oneor more of the sets of optimization results includes selecting a firstset of optimization results that prioritizes the sustainability controlobjective over the other control objective, a second set of optimizationresults that prioritizes the other control objective over thesustainability control objective, and a third set of optimizationresults that balances the sustainability control objective and the othercontrol objective.

In some embodiments, the operations further include presenting thevalues of the sustainability control objective and the other controlobjective associated with the first set of optimization results, thesecond set of optimization results, and the third set of optimizationresults as selectable options via a user interface. In some embodiments,the operations further include determining the selected set of theoptimization results responsive to a user selecting one of theselectable options via the user interface.

Another implementation of the present disclosure is a controller for aheating, ventilation, or air conditioning (HVAC) system for a building,according to some embodiments. In some embodiments, the controllerincludes one or more processors, and memory storing instructions that,when executed by the one or more processors, cause the one or moreprocessors to perform operations. In some embodiments, the operationsinclude obtaining one or more predictive models configured to predictvalues of a sustainability control objective and another controlobjective as a function of control decision variables for the HVACequipment. In some embodiments, the operations include executing aPareto optimization process using the one or more predictive models toproduce one or more sets of Pareto optimal values of the controldecision variables, the sustainability control objective, and the othercontrol objective. In some embodiments, the operations include operatingthe HVAC equipment to affect the environmental condition of the buildingin accordance with a selected set of the Pareto optimal values of thecontrol decision variables.

In some embodiments, executing the Pareto optimization process includesexecuting multiple optimization processes to produce corresponding setsof optimization results comprising values of the control decisionvariables, the sustainability control objective, and the other controlobjective. In some embodiments, executing the Pareto optimizationprocess further includes selecting, as the one or more sets of Paretooptimal values, one or more of the sets of optimization results forwhich the values of the sustainability control objective and the othercontrol objective are not both improved by another of the sets ofoptimization results.

In some embodiments, the sustainability control objective includes anamount of carbon emissions predicted to result from operating the HVACequipment in accordance with the control decision variables. In someembodiments, the other control objective includes at least one of aninfection risk predicted to result from operating the HVAC equipment inaccordance with the control decision variables, an operating costpredicted to result from operating the HVAC equipment in accordance withthe control decision variables, or a capital cost of purchasing orinstalling the HVAC equipment.

Those skilled in the art will appreciate that the summary isillustrative only and is not intended to be in any way limiting. Otheraspects, inventive features, and advantages of the devices and/orprocesses described herein, as defined solely by the claims, will becomeapparent in the detailed description set forth herein and taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing of a building equipped with a HVAC system, accordingto some embodiments.

FIG. 2 is a block diagram of an airside system which can be implementedin the building of FIG. 1, according to some embodiments.

FIG. 3 is a block diagram of an HVAC system including a controllerconfigured to operate an air-handling unit (AHU) of the HVAC system ofFIG. 1, according to some embodiments.

FIG. 4 is a block diagram illustrating the controller of FIG. 3 ingreater detail, showing operations performed when the controller is usedin an on-line mode or real-time implementation for making controldecisions to minimize energy consumption of the HVAC system and providesufficient disinfection, according to some embodiments.

FIG. 5 is a block diagram illustrating the controller of FIG. 3 ingreater detail, showing operations performed when the controller is usedin an off-line or planning mode for making design suggestions tominimize energy consumption of the HVAC system and provide sufficientdisinfection, according to some embodiments.

FIG. 6 is a flow diagram of a process which can be performed by thecontroller of FIG. 3 for determining control decisions for an HVACsystem to minimize energy consumption and provide sufficientdisinfection, according to some embodiments.

FIG. 7 is a flow diagram of a process which can be performed by thecontroller of FIG. 3 for determining design suggestions for an HVACsystem to minimize energy consumption and provide sufficientdisinfection, according to some embodiments.

FIG. 8 is a graph of various design suggestions or information that canbe provided by the controller of FIG. 3, according to some embodiments.

FIG. 9 is a drawing of a user interface that can be used to specifybuilding options and disinfection options and provide simulationresults, according to some embodiments.

FIG. 10 is a graph illustrating a technique which can be used by thecontroller of FIG. 3 to estimate a Pareto front of a tradeoff curve forrelative energy cost vs. infection probability, according to someembodiments.

FIG. 11 is a block diagram illustrating the controller of FIG. 3including a Pareto optimizer, according to some embodiments.

FIG. 12 is a block diagram illustrating the functionality of thecontroller of FIG. 11, according to some embodiments.

FIG. 13 is a diagram including a first graph that shows differentcombinations of decision variables, and a second graph that showssimulation results including energy cost and infection risk for each ofthe different combinations of decision variables, according to someembodiments.

FIG. 14 is a diagram including the second graph of FIG. 13 and a thirdgraph illustrating which of the simulation results are infeasible,feasible but not Pareto optimal, and feasible and Pareto optimal,according to some embodiments.

FIG. 15 is a diagram including the third graph of FIG. 14 and a fourthgraph that illustrates a minimum infection risk solution, a minimumenergy cost solution, and an equal priority infection risk/energy costsolution of the Pareto optimal simulation results, according to someembodiments.

FIG. 16 is a diagram including a first graph that shows differentcombinations of decision variables, and a second graph that showssimulation results including energy cost and infection risk for each ofthe different combinations of decision variables, according to someembodiments.

FIG. 17 is a flow diagram of a process for performing a Paretooptimization to determine different Pareto optimal solutions in terms ofenergy cost and infection risk for an HVAC system, according to someembodiments.

FIG. 18 is a flow diagram of a process for performing an infectionmetric analysis of an HVAC system over a previous time period, accordingto some embodiments.

FIG. 19 is a flow diagram of a process for performing a Paretooptimization in terms of energy cost and infection risk over a futuretime period, according to some embodiments.

FIG. 20 is a flow diagram of a process for performing an infectionmetrics analysis of an HVAC system over a previous time period and aPareto optimization for the HVAC system over a future time period,according to some embodiments.

FIG. 21 is a user interface showing results of an infection metricanalysis for display on a user device, according to some embodiments.

FIG. 22 is a user interface showing results of the Pareto optimizationof FIG. 17 or 19, according to some embodiments.

FIG. 23 is a user interface showing operating adjustments for a buildingadministrator to perform as a result of the Pareto optimization of FIG.17 or 19, according to some embodiments.

FIG. 24 is a diagram including a first graph that shows differentcombinations of decision variables, and a second graph that showssimulation results including a sustainability metric and infection riskfor each of the different combinations of decision variables, accordingto some embodiments.

FIG. 25 is a graph showing a relationship between energy cost and acarbon equivalent, according to some embodiments.

FIG. 26 is another graph showing a relationship between total cost and acarbon equivalent, according to some embodiments.

FIG. 27 is a block diagram illustrating the functionality of thecontroller of FIG. 11 including functionality for converting betweenenergy cost and a sustainability metric, according to some embodiments.

FIG. 28 is a flow diagram of a process for performing a Paretooptimization to determine different Pareto optimal solutions in terms ofenergy cost converted to a sustainability metric and infection risk foran HVAC system, according to some embodiments.

FIG. 29 is a flow diagram of a process for performing a Paretooptimization to determine different Pareto optimal solutions in terms ofa sustainability metric and infection risk for an HVAC system, accordingto some embodiments.

FIG. 30 is a diagram including a first graph that shows differentcombinations of decision variables, and a second graph that showssimulation results including a sustainability metric and an energy costfor each of the different combinations of decision variables, accordingto some embodiments.

DETAILED DESCRIPTION Overview

Referring generally to the FIGURES, systems and methods for minimizingenergy consumption of an HVAC system while maintaining a desired levelof disinfection are shown. The system may include an AHU that servesmultiple zones, a controller, one or more UV lights that disinfect airbefore it is provided from the AHU to the zones, and/or a filter that isconfigured to filter air to provide additional disinfection for the airbefore it is provided to the zones. In some embodiments, the system alsoincludes one or more zone sensors (e.g., temperature and/or humiditysensors, etc.) and one or more ambient or outdoor sensors (e.g., outdoortemperature and/or outdoor humidity sensors, etc.).

The controller uses a model-based design and optimization framework tointegrate building disinfection control with existing temperatureregulation in building HVAC systems. The controller uses the Wells-Rileyequation to transform a required upper limit of infection probabilityinto constraints on indoor concentration of infectious particles,according to some embodiments. In some embodiments, the controller usesa dynamic model for infectious agent concentration to impose theseconstraints on an optimization problem similar to temperature andhumidity constraints. By modeling effects of various types of optionalinfection control equipment (e.g., UV lights and/or filters), thecontroller may utilize a combination of fresh-air ventilation and directfiltration/disinfection to achieve desired infection constraints. Insome embodiments, the controller can use this composite model foroptimal design (e.g., in an off-line implementation of the controller)to determine which additional disinfection strategies are desirable,cost effective, or necessary. The controller can also be used foron-line control to determine control decisions for various controllableequipment (e.g., dampers of the AHU) in real-time to minimize energyconsumption or energy costs of the HVAC system while meetingtemperature, humidity, and infectious quanta concentration constraints.

The systems and methods described herein treat infection control as anintegral part of building HVAC operation rather than a short term orindependent control objective, according to some embodiments. While itmay be possible to achieve disinfection by the addition of UV lights andfilters running at full capacity, such a strategy may be costly andconsume excessive amounts of energy. However, the systems and methodsdescribed herein couple both objectives (disinfection control andminimal energy consumption) to assess optimal design and operationaldecisions on a case-by-case basis also taking into account climate,energy and disinfection goals of particular buildings.

The controller can be implemented in an off-line mode as a design tool.With the emergence of various strategies for building disinfection,building designers and operators now have a wide array of options forretrofitting a building to reduce the spread of infectious diseases tobuilding occupants. This is typically accomplished by lowering theconcentration of infectious particles in the air space, which can beaccomplished by killing the microbes via UV radiation, trapping them viafiltration, or simply forcing them out of the building via fresh-airventilation. While any one of these strategies individually can providedesired levels of disinfection, it may do so at unnecessarily high costor with negative consequences for thermal comfort of building occupants.Thus, to help evaluate the tradeoff and potential synergies between thevarious disinfection options, the model-based design tool can estimateannualized capital and energy costs for a given set of disinfectionequipment. For a given AHU, this includes dynamic models fortemperature, humidity, and infectious particle concentration, and itemploys the Wells-Riley infection equation to enforce constraints onmaximum occupant infection probability. By being able to quicklysimulate a variety of simulation instances, the controller (whenoperating as the design tool in the off-line mode) can present buildingdesigners with the tradeoff between cost and disinfection, allowing themto make informed decisions about retrofit.

A key feature of the design tool is that it shows to what extent theinherent flexibility of the existing HVAC system can be used to providedisinfection. In particular, in months when infectivity is of biggestconcern, a presence of free cooling from fresh outdoor air means thatthe energy landscape is relatively flat regardless of how the controllerdetermines to operate the HVAC system. Thus, the controller couldpotentially increase fresh-air intake significantly to providesufficient disinfection without UV or advanced filtration whileincurring only a small energy penalty. The design tool can provideestimates to customers to allow them to make informed decisions aboutwhat additional disinfection equipment (if any) to install and thenprovide the modified control systems needed to implement the desiredinfection control.

The controller can also be implemented in an on-line mode as a real-timecontroller. Although equipment like UV lamps and advanced filtration canbe installed in buildings to mitigate the spread of infectious diseases,it is often unclear how to best operate that equipment to achievedesired disinfection goals in a cost-effective manner. A common strategyis to take the robust approach of opting for the highest-efficiencyfilters and running UV lamps constantly. While this strategy will indeedreduce infection probability to its lowest possible value, it is likelyto do so at exorbitant cost due to the constant energy penalties of bothstrategies. Building managers may potentially choose to completelydisable filters and UV lamps to conserve energy consumption. Thus, thebuilding may end up in a worst-of-both-words situation where thebuilding manager has paid for disinfection equipment but the zones areno longer receiving any disinfection. To remove this burden frombuilding operators, the controller can automate infection control byintegrating disinfection control (e.g., based on the Wells-Rileyequation) in a model based control scheme. In this way, the controllercan simultaneously achieve thermal comfort and provide adequatedisinfection at the lowest possible cost given currently availableequipment.

Advantageously, the control strategy can optimize in real time theenergy and disinfection tradeoffs of all possible control variables.Specifically, the controller may choose to raise fresh-air intakefraction even though it incurs a slight energy penalty because it allowsa significant reduction of infectious particle concentrations whilestill maintaining comfortable temperatures. Thus, in some climates itmay be possible to provide disinfection without additional equipment,but this strategy is only possible if the existing controlinfrastructure can be guided or constrained so as to provide desireddisinfection. Alternatively, in buildings that have chosen to add UVlamps and/or filtration, the controller can find the optimal combinationof techniques to achieve desired control objectives at the lowestpossible cost. In addition, because the constraint on infectionprobability is configurable, the controller can empower buildingoperators to make their own choices regarding disinfection and energyuse (e.g. opting for a loose constraint in the summer when disease israre and energy use is intensive, while transitioning to a tightconstraint in winter when disease is prevalent and energy less of aconcern). Advantageously, the controller can provide integrated comfort,disinfection, and energy management to customers to achieve betteroutcomes in all three areas compared to other narrow and individualsolutions.

In some embodiments, the models used to predict temperature, humidity,and/or infectious quanta are dynamic models. The term “dynamic model”and variants thereof (e.g., dynamic temperature model, dynamic humiditymodel, dynamic infectious quanta model, etc.) are used throughout thepresent disclosure to refer to any type of model that predicts the valueof a quantity (e.g., temperature, humidity, infectious quanta) atvarious points in time as a function of zero or more input variables. Adynamic model may be “dynamic” as a result of the input variableschanging over time even if the model itself does not change. Forexample, a steady-state model that uses ambient temperature or any othervariable that changes over time as an input may be considered a dynamicmodel. Dynamic models may also include models that vary over time. Forexample, models that are retrained periodically, configured to adapt tochanging conditions over time, and/or configured to use differentrelationships between input variables and predicted outputs (e.g., afirst set of relationships for winter months and a second set ofrelationships for summer months) may also be considered dynamic models.Dynamic models may also include ordinary differential equation (ODE)models or other types of models having input variables that change overtime and/or input variables that represent the rate of change of avariable.

Building and HVAC System

Referring now to FIG. 1, a perspective view of a building 10 is shown.Building 10 can be served by a building management system (BMS). A BMSis, in general, a system of devices configured to control, monitor, andmanage equipment in or around a building or building area. A BMS caninclude, for example, a HVAC system, a security system, a lightingsystem, a fire alerting system, any other system that is capable ofmanaging building functions or devices, or any combination thereof. Anexample of a BMS which can be used to monitor and control building 10 isdescribed in U.S. patent application Ser. No. 14/717,593 filed May 20,2015, the entire disclosure of which is incorporated by referenceherein.

The BMS that serves building 10 may include a HVAC system 100. HVACsystem 100 can include a plurality of HVAC devices (e.g., heaters,chillers, air handling units, pumps, fans, thermal energy storage, etc.)configured to provide heating, cooling, ventilation, or other servicesfor building 10. For example, HVAC system 100 is shown to include awaterside system 120 and an airside system 130. Waterside system 120 mayprovide a heated or chilled fluid to an air handling unit of airsidesystem 130. Airside system 130 may use the heated or chilled fluid toheat or cool an airflow provided to building 10. In some embodiments,waterside system 120 can be replaced with or supplemented by a centralplant or central energy facility (described in greater detail withreference to FIG. 2). An example of an airside system which can be usedin HVAC system 100 is described in greater detail with reference to FIG.2.

HVAC system 100 is shown to include a chiller 102, a boiler 104, and arooftop air handling unit (AHU) 106. Waterside system 120 may use boiler104 and chiller 102 to heat or cool a working fluid (e.g., water,glycol, etc.) and may circulate the working fluid to AHU 106. In variousembodiments, the HVAC devices of waterside system 120 can be located inor around building 10 (as shown in FIG. 1) or at an offsite locationsuch as a central plant (e.g., a chiller plant, a steam plant, a heatplant, etc.). The working fluid can be heated in boiler 104 or cooled inchiller 102, depending on whether heating or cooling is required inbuilding 10. Boiler 104 may add heat to the circulated fluid, forexample, by burning a combustible material (e.g., natural gas) or usingan electric heating element. Chiller 102 may place the circulated fluidin a heat exchange relationship with another fluid (e.g., a refrigerant)in a heat exchanger (e.g., an evaporator) to absorb heat from thecirculated fluid. The working fluid from chiller 102 and/or boiler 104can be transported to AHU 106 via piping 108.

AHU 106 may place the working fluid in a heat exchange relationship withan airflow passing through AHU 106 (e.g., via one or more stages ofcooling coils and/or heating coils). The airflow can be, for example,outside air, return air from within building 10, or a combination ofboth. AHU 106 may transfer heat between the airflow and the workingfluid to provide heating or cooling for the airflow. For example, AHU106 can include one or more fans or blowers configured to pass theairflow over or through a heat exchanger containing the working fluid.The working fluid may then return to chiller 102 or boiler 104 viapiping 110.

Airside system 130 may deliver the airflow supplied by AHU 106 (i.e.,the supply airflow) to building 10 via air supply ducts 112 and mayprovide return air from building 10 to AHU 106 via air return ducts 114.In some embodiments, airside system 130 includes multiple variable airvolume (VAV) units 116. For example, airside system 130 is shown toinclude a separate VAV unit 116 on each floor or zone of building 10.VAV units 116 can include dampers or other flow control elements thatcan be operated to control an amount of the supply airflow provided toindividual zones of building 10. In other embodiments, airside system130 delivers the supply airflow into one or more zones of building 10(e.g., via supply ducts 112) without using intermediate VAV units 116 orother flow control elements. AHU 106 can include various sensors (e.g.,temperature sensors, pressure sensors, etc.) configured to measureattributes of the supply airflow. AHU 106 may receive input from sensorslocated within AHU 106 and/or within the building zone and may adjustthe flow rate, temperature, or other attributes of the supply airflowthrough AHU 106 to achieve setpoint conditions for the building zone.

Airside System

Referring now to FIG. 2, a block diagram of an airside system 200 isshown, according to some embodiments. In various embodiments, airsidesystem 200 may supplement or replace airside system 130 in HVAC system100 or can be implemented separate from HVAC system 100. Whenimplemented in HVAC system 100, airside system 200 can include a subsetof the HVAC devices in HVAC system 100 (e.g., AHU 106, VAV units 116,ducts 112-114, fans, dampers, etc.) and can be located in or aroundbuilding 10. Airside system 200 may operate to heat, cool, humidify,dehumidify, filter, and/or disinfect an airflow provided to building 10in some embodiments.

Airside system 200 is shown to include an economizer-type air handlingunit (AHU) 202. Economizer-type AHUs vary the amount of outside air andreturn air used by the air handling unit for heating or cooling. Forexample, AHU 202 may receive return air 204 from building zone 206 viareturn air duct 208 and may deliver supply air 210 to building zone 206via supply air duct 212. In some embodiments, AHU 202 is a rooftop unitlocated on the roof of building 10 (e.g., AHU 106 as shown in FIG. 1) orotherwise positioned to receive both return air 204 and outside air 214.AHU 202 can be configured to operate exhaust air damper 216, mixingdamper 218, and outside air damper 220 to control an amount of outsideair 214 and return air 204 that combine to form supply air 210. Anyreturn air 204 that does not pass through mixing damper 218 can beexhausted from AHU 202 through exhaust damper 216 as exhaust air 222.

Each of dampers 216-220 can be operated by an actuator. For example,exhaust air damper 216 can be operated by actuator 224, mixing damper218 can be operated by actuator 226, and outside air damper 220 can beoperated by actuator 228. Actuators 224-228 may communicate with an AHUcontroller 230 via a communications link 232. Actuators 224-228 mayreceive control signals from AHU controller 230 and may provide feedbacksignals to AHU controller 230. Feedback signals can include, forexample, an indication of a current actuator or damper position, anamount of torque or force exerted by the actuator, diagnosticinformation (e.g., results of diagnostic tests performed by actuators224-228), status information, commissioning information, configurationsettings, calibration data, and/or other types of information or datathat can be collected, stored, or used by actuators 224-228. AHUcontroller 230 can be an economizer controller configured to use one ormore control algorithms (e.g., state-based algorithms, extremum seekingcontrol (ESC) algorithms, proportional-integral (PI) control algorithms,proportional-integral-derivative (PID) control algorithms, modelpredictive control (MPC) algorithms, feedback control algorithms, etc.)to control actuators 224-228.

Still referring to FIG. 2, AHU 202 is shown to include a cooling coil234, a heating coil 236, and a fan 238 positioned within supply air duct212. Fan 238 can be configured to force supply air 210 through coolingcoil 234 and/or heating coil 236 and provide supply air 210 to buildingzone 206. AHU controller 230 may communicate with fan 238 viacommunications link 240 to control a flow rate of supply air 210. Insome embodiments, AHU controller 230 controls an amount of heating orcooling applied to supply air 210 by modulating a speed of fan 238. Insome embodiments, AHU 202 includes one or more air filters (e.g., filter308) and/or one or more ultraviolet (UV) lights (e.g., UV lights 306) asdescribed in greater detail with reference to FIG. 3. AHU controller 230can be configured to control the UV lights and route the airflow throughthe air filters to disinfect the airflow as described in greater detailbelow.

Cooling coil 234 may receive a chilled fluid from central plant 200(e.g., from cold water loop 216) via piping 242 and may return thechilled fluid to central plant 200 via piping 244. Valve 246 can bepositioned along piping 242 or piping 244 to control a flow rate of thechilled fluid through cooling coil 234. In some embodiments, coolingcoil 234 includes multiple stages of cooling coils that can beindependently activated and deactivated (e.g., by AHU controller 230, byBMS controller 266, etc.) to modulate an amount of cooling applied tosupply air 210.

Heating coil 236 may receive a heated fluid from central plant 200(e.g., from hot water loop 214) via piping 248 and may return the heatedfluid to central plant 200 via piping 250. Valve 252 can be positionedalong piping 248 or piping 250 to control a flow rate of the heatedfluid through heating coil 236. In some embodiments, heating coil 236includes multiple stages of heating coils that can be independentlyactivated and deactivated (e.g., by AHU controller 230, by BMScontroller 266, etc.) to modulate an amount of heating applied to supplyair 210.

Each of valves 246 and 252 can be controlled by an actuator. Forexample, valve 246 can be controlled by actuator 254 and valve 252 canbe controlled by actuator 256. Actuators 254-256 may communicate withAHU controller 230 via communications links 258-260. Actuators 254-256may receive control signals from AHU controller 230 and may providefeedback signals to controller 230. In some embodiments, AHU controller230 receives a measurement of the supply air temperature from atemperature sensor 262 positioned in supply air duct 212 (e.g.,downstream of cooling coil 334 and/or heating coil 236). AHU controller230 may also receive a measurement of the temperature of building zone206 from a temperature sensor 264 located in building zone 206.

In some embodiments, AHU controller 230 operates valves 246 and 252 viaactuators 254-256 to modulate an amount of heating or cooling providedto supply air 210 (e.g., to achieve a setpoint temperature for supplyair 210 or to maintain the temperature of supply air 210 within asetpoint temperature range). The positions of valves 246 and 252 affectthe amount of heating or cooling provided to supply air 210 by coolingcoil 234 or heating coil 236 and may correlate with the amount of energyconsumed to achieve a desired supply air temperature. AHU 230 maycontrol the temperature of supply air 210 and/or building zone 206 byactivating or deactivating coils 234-236, adjusting a speed of fan 238,or a combination of both.

Still referring to FIG. 2, airside system 200 is shown to include abuilding management system (BMS) controller 266 and a client device 268.BMS controller 266 can include one or more computer systems (e.g.,servers, supervisory controllers, subsystem controllers, etc.) thatserve as system level controllers, application or data servers, headnodes, or master controllers for airside system 200, central plant 200,HVAC system 100, and/or other controllable systems that serve building10. BMS controller 266 may communicate with multiple downstream buildingsystems or subsystems (e.g., HVAC system 100, a security system, alighting system, central plant 200, etc.) via a communications link 270according to like or disparate protocols (e.g., LON, BACnet, etc.). Invarious embodiments, AHU controller 230 and BMS controller 266 can beseparate (as shown in FIG. 2) or integrated. In an integratedimplementation, AHU controller 230 can be a software module configuredfor execution by a processor of BMS controller 266.

In some embodiments, AHU controller 230 receives information from BMScontroller 266 (e.g., commands, setpoints, operating boundaries, etc.)and provides information to BMS controller 266 (e.g., temperaturemeasurements, valve or actuator positions, operating statuses,diagnostics, etc.). For example, AHU controller 230 may provide BMScontroller 266 with temperature measurements from temperature sensors262-264, equipment on/off states, equipment operating capacities, and/orany other information that can be used by BMS controller 266 to monitoror control a variable state or condition within building zone 206.

Client device 268 can include one or more human-machine interfaces orclient interfaces (e.g., graphical user interfaces, reportinginterfaces, text-based computer interfaces, client-facing web services,web servers that provide pages to web clients, etc.) for controlling,viewing, or otherwise interacting with HVAC system 100, its subsystems,and/or devices. Client device 268 can be a computer workstation, aclient terminal, a remote or local interface, or any other type of userinterface device. Client device 268 can be a stationary terminal or amobile device. For example, client device 268 can be a desktop computer,a computer server with a user interface, a laptop computer, a tablet, asmartphone, a PDA, or any other type of mobile or non-mobile device.Client device 268 may communicate with BMS controller 266 and/or AHUcontroller 230 via communications link 272.

HVAC System with Building Infection Control

Overview

Referring particularly to FIG. 3, a HVAC system 300 that is configuredto provide disinfection for various zones of a building (e.g., building10) is shown, according to some embodiments. HVAC system 300 can includean air handling unit (AHU) 304 (e.g., AHU 230, AHU 202, etc.) that canprovide conditioned air (e.g., cooled air, supply air 210, etc.) tovarious building zones 206. The AHU 304 may draw air from the zones 206in combination with drawing air from outside (e.g., outside air 214) toprovide conditioned or clean air to zones 206. The HVAC system 300includes a controller 310 (e.g., AHU controller 230) that is configuredto determine a fraction × of outdoor air to recirculated air that theAHU 304 should use to provide a desired amount of disinfection tobuilding zones 206. In some embodiments, controller 310 can generatecontrol signals for various dampers of AHU 304 so that AHU 304 operatesto provide the conditioned air to building zones 206 using the fraction×.

The HVAC system 300 can also include ultraviolet (UV) lights 306 thatare configured to provide UV light to the conditioned air before it isprovided to building zones 206. The UV lights 306 can providedisinfection as determined by controller 310 and/or based on useroperating preferences. For example, the controller 310 can determinecontrol signals for UV lights 306 in combination with the fraction x ofoutdoor air to provide a desired amount of disinfection and satisfy aninfection probability constraint. Although UV lights 306 are referred tothroughout the present disclosure, the systems and methods describedherein can use any type of disinfection lighting using any frequency,wavelength, or luminosity of light effective for disinfection. It shouldbe understood that UV lights 306 (and any references to UV lights 306throughout the present disclosure) can be replaced with disinfectionlighting of any type without departing from the teachings of the presentdisclosure.

The HVAC system 300 can also include one or more filters 308 orfiltration devices (e.g., air purifiers). In some embodiments, thefilters 308 are configured to filter the conditioned air or recirculatedair before it is provided to building zones 206 to provide a certainamount of disinfection. In this way, controller 310 can perform anoptimization in real-time or as a planning tool to determine controlsignals for AHU 304 (e.g., the fraction x) and control signals for UVlights 306 (e.g., on/off commands) to provide disinfection for buildingzones 206 and reduce a probability of infection of individuals that areoccupying building zones 206. Controller 310 can also function as adesign tool that is configured to determine suggestions for buildingmanagers regarding benefits of installing or using filters 308, and/orspecific benefits that may arise from using or installing a particulartype or size of filter. Controller 310 can thereby facilitate informeddesign decisions to maintain sterilization of air that is provided tobuilding zones 206 and reduce a likelihood of infection or spreading ofinfectious matter.

Wells-Riley Airborne Transmission

The systems and methods described herein may use an infectionprobability constraint in various optimizations (e.g., in on-line orreal-time optimizations or in off-line optimizations) to facilitatereducing infection probability among residents or occupants of spacesthat the HVAC system serves. The infection probability constraint can bebased on a steady-state Wells-Riley equation for a probability ofairborne transmission of an infectious agent given by:

$P:={\frac{D}{S} = {1 - {\exp\;\left( {- \frac{Ipqt}{Q}} \right)}}}$

where P is a probability that an individual becomes infected (e.g., in azone, space, room, environment, etc.), D is a number of infectedindividuals (e.g., in the zone, space, room, environment, etc.), S is atotal number of susceptible individuals (e.g., in the zone, space, room,environment, etc.), I is a number of infectious individuals (e.g., inthe zone, space, room, environment, etc.), q is a disease quantageneration rate (e.g., with units of 1/sec), p is a volumetric breathrate of one individual (e.g., in m³/sec), t is a total exposure time(e.g., in seconds), and Q is an outdoor ventilation rate (e.g., inm³/sec). For example, Q may be a volumetric flow rate of fresh outdoorair that is provided to the building zones 206 by AHU 304.

When the Wells-Riley equation is implemented by controller 310 asdescribed herein, controller 310 may use the Wells-Riley equation (or adynamic version of the Wells-Riley equation) to determine an actual orcurrent probability of infection P and operate the HVAC system 200 tomaintain the actual probability of infection P below (or drive theactual probability of infection below) a constraint or maximum allowablevalue. The constraint value (e.g., P_(max)) may be a constant value, ormay be adjustable by a user (e.g., a user-set value). For example, theuser may set the constraint value of the probability of infection to amaximum desired probability of infection (e.g., either for on-lineimplementation of controller 310 to maintain the probability ofinfection below the maximum desired probability, or for an off-lineimplementation/simulation performed by controller 310 to determinevarious design parameters for HVAC system 200 such as filter size), ormay select from various predetermined values (e.g., 3-5 differentchoices of the maximum desired probability of infection).

In some embodiments, the number of infectious individuals I can bedetermined by controller 310 based on data from the Centers for Diseaseand Control Prevention or a similar data source. The value of I may betypically set equal to 1 but may vary as a function of occupancy ofbuilding zones 206.

The disease quanta generation rate q may be a function of the infectiousagent. For example, more infectious diseases may have a higher value ofq, while less infectious diseases may have a lower value of q. Forexample, the value of q for COVID-19 may be 30-300 (e.g., 100).

The value of the volumetric breath rate p may be based on a type ofbuilding space 206. For example, the volumetric breath rate p may behigher if the building zone 206 is a gym as opposed to an officesetting. In general, an expected level of occupant activity maydetermine the value of the volumetric breath rate p.

A difference between D (the number of infected individuals) and I (thenumber of infectious individuals) is that D is a number of individualswho are infected (e.g., infected with a disease), while I is a number ofpeople that are infected and are actively contagious (e.g., individualsthat may spread the disease to other individuals or spread infectiousparticles when they exhale). The disease quanta generation rateindicates a number of infectious droplets that give a 63.2% chance ofinfecting an individual (e.g., 1−exp(−1)). For example, if an individualinhales k infectious particles, the probability that the individualbecomes infected (P) is given by

$1 - {\exp\left( {- \frac{k}{k_{0}}} \right)}$

where k is the number of infectious particles that the individual hasinhaled, and k₀ is a quantum of particles for a particular disease(e.g., a predefined value for different diseases). The quanta generationrate q is the rate at which quanta are generated (e.g., K/k₀) where K isthe rate of infectious particles exhaled by an infectious individual. Itshould be noted that values of the disease quanta generation rate q maybe back-calculated from epidemiological data or may be tabulated forwell-known diseases.

The Wells-Riley equation (shown above) is derived by assumingsteady-state concentrations for infectious particles in the air.Assuming a well-mixed space:

${V\frac{dN}{dt}} = {{Iq} - {NQ}}$

where V is a total air volume (e.g., in m³), N is a quantumconcentration in the air, I is the number of infectious individuals, qis the disease quanta generation rate, and Q is the outdoor ventilationrate. The term Iq is quanta production by infectious individuals (e.g.,as the individuals breathe out or exhale), and the term NQ is the quantaremoval rate due to ventilation (e.g., due to operation of AHU 304).

Assuming steady-state conditions, the steady state quantum concentrationin the air is expressed as:

$N_{ss} = \frac{Iq}{Q}$

according to some embodiments.

Therefore, if an individual inhales at an average rate of p (e.g., inm³/sec), over a period of length t the individual inhales a total volumept or N_(ss)ptk₀ infectious particles. Therefore, based on a probabilitymodel used to define the quanta, the infectious probability is given by:

$P = {{1 - {\exp\left( {- \frac{k}{k_{0}}} \right)}} = {{1 - {\exp\left( {{- N_{SS}}pt} \right)}} = {1 - {\exp\left( {- \frac{Iqpt}{Q}} \right)}}}}$

where P is the probability that an individual becomes infected, k is thenumber of infectious particles that the individual has inhaled, and k₀is the quantum of particles for the particular disease.

Carbon Dioxide for Infectious Particles Proxy

While the above equations may rely on in-air infectious quantaconcentration, measuring in-air infectious quanta concentration may bedifficult. However, carbon dioxide (CO2) is a readily-measureableparameter that can be a proxy species, measured by zone sensors 312. Insome embodiments, a concentration of CO2 in the zones 206 may bedirectly related to a concentration of the infectious quanta.

A quantity ϕ that defines a ratio of an infected particle concentrationin the building air to the infected particle concentration in theexhaled breath of an infectious individual is defined:

$\phi:=\frac{pN}{q}$

where p is the volumetric breath rate for an individual, N is thequantum concentration in the air, and q is the disease quanta generationrate. Deriving the above equation with respect to time yields:

$\frac{d\phi}{dt} = {{\frac{p}{q}\left( \frac{dN}{dt} \right)} = {\frac{Ip}{V} - {\phi\left( \frac{Q}{V} \right)}}}$

where p is the volumetric breath rate for the individual, q is diseasequanta generation rate, N is the quantum concentration in the air, t istime, I is the number of infectious individuals, V is the total airvolume, ϕ is the ratio, and Q is the outdoor ventilation rate. Since itcan be difficult to measure the ratio ϕ of the air, CO2 can be used as aproxy species.

Humans release CO2 when exhaling, which is ultimately transferred to theambient via ventilation of an HVAC system. Therefore, the differencebetween CO2 particles and infectious particles is that all individuals(and not only the infectious population) release CO2 and that theoutdoor air CO2 concentration is non-zero. However, it may be assumedthat the ambient CO2 concentration is constant with respect to time,which implies that a new quantity C can be defined as the net indoor CO2concentration (e.g., the indoor concentration minus the outdoorconcentration). With this assumption, the following differentialequation can be derived:

${V\frac{dC}{dt}} = {{Spc} - {QC}}$

where V is the total air volume (e.g., in m³), C is the net indoor CO2concentration, t is time, S is the total number of susceptibleindividuals (e.g., in building zone 206, or a modeled space, or all ofbuilding zones 206, or building 10), p is the volumetric breath rate forone individual, c is the net concentration of exhaled CO2, and Q is theoutdoor ventilation rate. This equation assumes that the only way toremove infectious particles is with fresh air ventilation (e.g., byoperating AHU 304 to draw outdoor air and use the outdoor air withrecirculated air). A new quantity ψ can be defined that gives the ratioof net CO2 concentration in the building air to net CO2 concentration inthe exhaled air:

$\psi = \frac{C}{c}$

where ψ is the ratio, C is the net indoor CO2 concentration, and c isthe net concentration of exhaled CO2.

Deriving the ratio ψ with respect to time yields:

$\frac{d\psi}{dt} = {{\frac{1}{c}\left( \frac{dC}{dt} \right)} = {\frac{Sp}{V} - {\psi\left( \frac{Q}{V} \right)}}}$

according to some embodiments.

Combining the above equation with the quantity ϕ, it can be derivedthat:

${\frac{d}{dt}{\log\left( \frac{\phi}{\psi} \right)}} = {{{\frac{1}{\phi}\left( \frac{d\phi}{dt} \right)} - {\frac{1}{\psi}\left( \frac{d\psi}{dt} \right)}} = {\frac{p}{V}\left( {\frac{I}{\phi} - \frac{S}{\psi}} \right)}}$

according to some embodiments. Assuming that the initial conditionsatisfies:

$\begin{matrix}{{\phi(0)} = {\frac{1}{S}{\psi(0)}}} & \;\end{matrix}$

it can be determined that the right-hand side of the

$\frac{d}{dt}{\log\left( \frac{\phi}{\psi} \right)}$

equation becomes zero. This implies that the term

$\log\left( \frac{\phi}{\psi} \right)$

and therefore

$\frac{\phi}{\psi}$

is a constant. Therefore, ϕ/ψ is constant for alltimes t and not merely initial conditions when t=0.

The

$\frac{d}{dt}{\log\left( \frac{\phi}{\psi} \right)}$

relationship only holds true when fresh outdoor air is used as the onlydisinfection mechanism. However, in many cases HVAC system 200 mayinclude one or more filters 308, and UV lights 306 that can be operatedto provide disinfection for building zones 206. If additional infectionmitigation strategies are used, the ventilation rate may instead by aneffective ventilation rate for infectious quanta that is different thanthat of the CO2. Additionally, the only way for the initial conditionsϕ(0) and ψ(0) to be in proportion is for both to be zero. Thisassumption can be reasonable if HVAC system 200 operates over aprolonged time period (such as overnight, when the concentrations havesufficient time to reach equilibrium zero values). However, ventilationis often partially or completely disabled overnight and therefore thetwo quantities ϕ and ψ are not related. However, CO2 concentration canbe measured to determine common model parameters (e.g., for the overallsystem volume V) without being used to estimate current infectiousparticle concentrations. If fresh outdoor air ventilation is the onlymechanism for disinfection of zones 206, and the HVAC system 200 is runso that the concentrations reach equilibrium, CO2 concentration can bemeasured and used to estimate current infectious particleconcentrations.

Dynamic Extension and Infection Probability Constraints

Referring still to FIG. 3, it may be desirable to model the infectiousquanta concentration N of building zones 206 as a dynamic parameterrather than assuming N is equal to the steady state N_(SS) value. Forexample, if infectious individuals enter building zones 206, leavebuilding zones 206, etc., the infectious quanta concentration N maychange over time. This can also be due to the fact that the effectivefresh air ventilation rate (which includes outdoor air intake as well asfiltration or UV disinfection that affects the infectious agentconcentration in the supply air that is provided by AHU 304 to zones206) can vary as HVAC system 200 operates.

Therefore, assuming that the infectious quanta concentration N(t) is atime-varying quantity, for a given time period t ∈[0, T], an individualbreathes in:

k _([0, T])=∫₀ ^(T) pk ₀ N(t) dt

where k_([0, T]) is the number of infectious particles that anindividual inhales over the given time period [0, T], p is thevolumetric breath rate of one individual, k₀ is the quantum of particlesfor a particular disease, and N(t) is the time-varying quantumconcentration of the infectious particle in the air.

Since

${P = {1 - {\exp\left( {- \frac{k}{k_{0}}} \right)}}},$

the above equation can be rearranged and substitution yields:

${- {\log\left( {1 - P_{\lbrack{0,T}\rbrack}} \right)}} = {{\int_{0}^{T}{p{N(t)}dt}} \approx {\Delta{\sum\limits_{t}{pN_{t}}}}}$

according to some embodiments.

Assuming an upper boundary P_([0,T]) ^(max) on acceptable or desirableinfection probability, a constraint is defined as:

${\frac{\Delta}{T}{\sum\limits_{t}N_{t}}} \leq {{- \frac{1}{pT}}{\log\left( {1 - P_{\lbrack{0,T}\rbrack}} \right)}}$

according to some embodiments. The constraint can define a fixed upperboundary on an average value of N_(t) over the given time interval.

Control Formulation

Referring particularly to FIG. 4, controller 310 is shown in greaterdetail, according to some embodiments. Controller 310 is configured togenerate control signals for any of UV lights 306, filter 308, and/orAHU 304. AHU 304 operates to draw outdoor air and/or recirculated air(e.g., from zones 206) to output conditioned (e.g., cooled) air. Theconditioned air may be filtered by passing through filter 308 (e.g.,which may include fans to draw the air through the filter 308) to outputfiltered air. The filtered air and/or the conditioned air can bedisinfected through operation of UV lights 306. The AHU 304, filter 308,and UV lights 306 can operate in unison to provide supply air to zones206.

Controller 310 includes a processing circuit 402 including a processor404 and memory 406. Processing circuit 402 can be communicably connectedwith a communications interface of controller 310 such that processingcircuit 402 and the various components thereof can send and receive datavia the communications interface. Processor 404 can be implemented as ageneral purpose processor, an application specific integrated circuit(ASIC), one or more field programmable gate arrays (FPGAs), a group ofprocessing components, or other suitable electronic processingcomponents.

Memory 406 (e.g., memory, memory unit, storage device, etc.) can includeone or more devices (e.g., RAM, ROM, Flash memory, hard disk storage,etc.) for storing data and/or computer code for completing orfacilitating the various processes, layers and modules described in thepresent application. Memory 406 can be or include volatile memory ornon-volatile memory. Memory 406 can include database components, objectcode components, script components, or any other type of informationstructure for supporting the various activities and informationstructures described in the present application. According to someembodiments, memory 406 is communicably connected to processor 404 viaprocessing circuit 402 and includes computer code for executing (e.g.,by processing circuit 402 and/or processor 404) one or more processesdescribed herein.

In some embodiments, controller 310 is implemented within a singlecomputer (e.g., one server, one housing, etc.). In various otherembodiments controller 310 can be distributed across multiple servers orcomputers (e.g., that can exist in distributed locations).

Memory 406 can include a constraint generator 410, a model manager 416,a sensor manager 414, an optimization manager 412, and a control signalgenerator 408. Sensor manager 414 can be configured to obtain zonesensor data from zone sensors 312 and/or ambient sensor data fromambient sensors 314 (e.g., environmental conditions, outdoortemperature, outdoor humidity, etc.) and distribute required sensor datato the various components of memory 406 thereof. Constraint generator410 is configured to generate one or more constraints for anoptimization problem (e.g., an infection probability constraint) andprovide the constraints to optimization manager 412. Model manager 416can be configured to generate dynamic models (e.g., individual orzone-by-zone dynamic models, aggregate models, etc.) and provide thedynamic models to optimization manager 412. Optimization manager 412 canbe configured to use the constraints provided by constraint generator410 and the dynamic models provided by model manager 416 to formulate anoptimization problem. Optimization manager 412 can also define anobjective function for the optimization problem, and minimize oroptimize the objective function subject to the one or more constraintsand the dynamic models. The objective function may be a function thatindicates an amount of energy consumption, energy consumption costs,carbon footprint, or any other optimization goals over a time intervalor time horizon (e.g., a future time horizon) as a function of variouscontrol decisions. Optimization manager 412 can output optimizationsresults to control signal generator 408. Control signal generator 408can generate control signals based on the optimization results andprovide the control signals to any of AHU 304, filter 308, and/or UVlights 306.

Referring particularly to FIGS. 3 and 4, AHU 304 can be configured toserve multiple building zones 206. For example, AHU 304 can beconfigured to serve a collection of zones 206 that are numbered k=1, . .. , K. Each zone 206 can have a temperature, referred to as temperatureT_(k) (the temperature of the kth zone 206), a humidity ω_(k) (thehumidity of the kth zone 206), and an infectious quanta concentrationN_(k) (the infectious quanta concentration of the kth zone 206). Usingthis notation, the following dynamic models of individual zones 206 canbe derived:

${{\rho c{V_{k}\left( \frac{dT_{k}}{dt} \right)}} = {{\rho c{f_{k}\left( {T_{0} - T_{k}} \right)}} + {Q_{k}\left( T_{k} \right)}}}{{\rho{V_{k}\left( \frac{d\omega_{k}}{dt} \right)}} = {{\rho{f\left( {\omega_{0} - T_{0}} \right)}} + w_{k}}}{{V_{k}\left( \frac{dN_{k}}{dt} \right)} = {{f_{k}\left( {N_{0} - N_{k}} \right)} + {I_{k}q}}}$

where f_(k) is a volumetric flow of air into the kth zone, ρ is a massdensity of air (e.g., in kg per cubic meters), c is the heat capacity ofair (e.g., in kJ/kg·K), Q_(k)(·) is heat load on the kth zone 206 (whichmay depend on the temperature T_(k)), w_(k) is the moisture gain of thekth zone 206, and I_(k) is the number of infectious individuals in thekth zone 206. T₀ is the temperature of the air provided to the kth zone(e.g., as discharged by a VAV box of AHU 304), ω₀ is the humidity of theair provided to the kth zone 206, and N₀ is the infectious quantaconcentration of the air provided to the kth zone 206.

The temperature T₀ of air output by the AHU 304, the humidity ω₀ of airoutput by the AHU 304, and the infectious quanta concentration N₀ of airoutput by the AHU 304 is calculated using the equations:

${T_{0} = {{xT_{a}} + {\left( {1 - x} \right)\frac{\sum_{k}{f_{k}T_{k}}}{\sum_{k}f_{k}}} - {\Delta T_{c}}}}{\omega_{0} = {{x\omega_{a}} + {\left( {1 - x} \right)\frac{\sum_{k}{f_{k}\omega_{k}}}{\sum_{k}f_{k}}} - {\Delta\omega_{c}}}}{N_{0} = {\left( {1 - \lambda} \right)\left( {1 - x} \right)\frac{\sum_{k}{f_{k}N_{k}}}{\Sigma_{k}f_{k}}}}$

where x is the fresh-air intake fraction of AHU 304, T_(a) is currentambient temperature, ω_(a) is current ambient humidity, ΔT_(c) istemperature reductions from the cooling coil of AHU 304, Δω_(c) ishumidity reduction from the cooling coil of AHU 304, and λ is afractional reduction of infectious quanta due to filtration (e.g.,operation of filter 308) and/or UV treatment (e.g., operation of UVlights 306) at AHU 304 (but not due to ventilation which is accountedfor in the factor 1−x, according to some embodiments.

In some embodiments, the dynamic models of the individual zones arestored by and used by model manager 416. Model manager 416 can store theindividual dynamic models shown above and/or aggregated models(described in greater detail below) and populate the models. Thepopulated models can then be provided by model manager 416 tooptimization manager 412 for use in performing an optimization.

In some embodiments, model manager 416 is configured to receive sensordata from sensor manager 414. Sensor manager 414 may receive sensor datafrom zone sensors 312 and/or ambient sensors 313 and provide appropriateor required sensor data to the various managers, modules, generators,components, etc., of memory 406. For example, sensor manager 414 canobtain values of the current ambient temperature T_(a), the currentambient humidity ω_(a), the temperature reduction ΔT_(c) resulting fromthe cooling coil of AHU 304, and/or the humidity reduction Δω_(c)resulting from the cooling coil of AHU 304, and provide these values tomodel manager 416 for use in determining T₀, ω₀, and N₀ or forpopulating the dynamic models of the individual zones 206.

In some embodiments, various parameters or values of the variables ofthe dynamic models of the individual zones 206 are predefined,predetermined, or stored values, or may be determined (e.g., using afunction, an equation, a table, a look-up table, a graph, a chart, etc.)based on sensor data (e.g., current environmental conditions of theambient or outdoor area, environmental conditions of the zones 206,etc.). For example, the mass density of air ρ may be a predeterminedvalue or may be determined based on sensor data. In some embodiments,model manager 416 can use stored values, sensor data, etc., to fullypopulate the dynamic models of the individual zones 206 (except forcontrol or adjustable variables of the dynamic models of the individualzones 206 that are determined by performing the optimization). Once themodels are populated so that only the control variables remain undefinedor undetermined, model manager 416 can provide the populated models tooptimization manager 412.

The number of infectious individuals I_(k) can be populated based onsensor data (e.g., based on biometric data of occupants or individualsof the building zones 206), or can be estimated based on sensor data. Insome embodiments, model manager 416 can use an expected number ofoccupants and various database regarding a number of infectedindividuals in an area. For example, model manager 416 can query anonline database regarding potential infection spread in the area (e.g.,number of positive tests of a particular virus or contagious illness)and estimate if it is likely that an infectious individual is in thebuilding zone 206.

In some embodiments, it can be difficult to obtain zone-by-zone valuesof the number of infectious individuals I_(k) in the modeled space(e.g., the zones 206). In some embodiments, model manager 416 isconfigured to use an overall approximation of the model for N_(k). Modelmanager 416 can store and use volume-averaged variables:

$\overset{\_}{N} = \frac{\sum_{k}{V_{k}N_{k}}}{\overset{\_}{V}}$$\overset{\_}{f} = {\sum\limits_{k}f_{k}}$$\overset{\_}{V} = {\sum\limits_{k}V_{k}}$$\overset{\_}{I} = {\sum\limits_{k}I_{k}}$

according to some embodiments. Specifically, the equations shown aboveaggregate the variables N, f, V, and Ī across multiple zones 206 bycalculating a weighted average based on the volume of zones 206.

The K separate ordinary differential equation models (i.e., the dynamicmodels of the individual zones 206) can be added for N_(k) to determinean aggregate quantum concentration model:

$\begin{matrix}{{\overset{\_}{V}\frac{d\overset{\_}{N}}{dt}} = {\sum\limits_{k}{V_{k}\frac{dN_{k}}{dt}}}} \\{= {\sum\limits_{k}\left( {{f_{k}\left( {N_{0} - N_{k}} \right)} + {I_{k}q}} \right)}} \\{= {{\overset{\_}{I}q} + {\sum\limits_{k}{f_{k}\left( {{\left( {1 - \lambda} \right)\left( {1 - x} \right)\frac{\sum_{k\;\prime}{f_{k\;\prime}N_{k\;\prime}}}{\sum_{k\;\prime}f_{k\;\prime}}} - N_{k}} \right)}}}} \\{= {{\overset{\_}{I}q} + {\left( {1 - \lambda} \right)\left( {1 - x} \right){\sum\limits_{k\;\prime}{f_{k\;\prime}\ N_{k\;\prime}}}}\  - {\sum\limits_{k}{f_{k}N_{k}}}}} \\{= {{\overset{\_}{I}q} - {\left( {\lambda + x - {\lambda x}} \right){\sum\limits_{k}{f_{k}N_{k}}}}}} \\{\approx {{\overset{\_}{I}q} - {\left( {\lambda + x - {\lambda x}} \right)\overset{\_}{fN}}}}\end{matrix}$

according to some embodiments, assuming that N_(k)≈N for each zone 206.The aggregate quantum concentration model is shown below:

${\overset{\_}{V}\frac{d\overset{\_}{N}}{dt}} = {{{\overset{\_}{I}q} - {\left( {\lambda + x - {\lambda x}} \right){\sum\limits_{k}{f_{k}N_{k}}}}} \approx {{\overset{\_}{I}q} - {\left( {\lambda + x - {\lambda x}} \right)\overset{\_}{fN}}}}$

according to some embodiments.

Defining aggregate temperature, humidity, heat load, and moisture gainparameters:

$\overset{\_}{T} = \frac{\sum_{k}{V_{k}T_{k}}}{\overset{\_}{V}}$$\overset{\_}{\omega} = \frac{\sum_{k}{V_{k}\omega_{k}}}{\overset{\_}{V}}$${\overset{\_}{Q}( \cdot )} = {\sum\limits_{k}{Q_{k}( \cdot )}}$$\overset{\_}{w} = {\sum\limits_{k}w_{k}}$

allows the k thermal models

$\rho c{V_{k}\left( \frac{dT_{k}}{dt} \right)}$

to be added:

$\begin{matrix}{{\rho\; c\overset{\_}{V}\frac{d\overset{\_}{T}}{dC}} = {\sum\limits_{k}{\rho\;{cV}_{k}\frac{dT_{k}}{dt}}}} \\{= {\sum\limits_{k}\left( {{\rho\;{{cf}_{k}\left( {T_{0} - T_{k}} \right)}} + {Q_{k}\left( T_{k} \right)}} \right)}} \\{= {{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {\sum\limits_{k}{\rho\;{{cf}_{k}\left( {{xT}_{a} + {\left( {1 - x} \right)\frac{\sum_{k\;\prime}{f_{k\;\prime}T_{k\;\prime}}}{\sum_{k\;\prime}f_{k\;\prime}}} - T_{k} - {\Delta T_{c}}} \right)}}}}} \\{= {{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {\left( {1 - x} \right){\sum\limits_{k\;\prime}{\rho\;{cf}_{k\;\prime}T_{k\;\prime}}}}\  + {\sum\limits_{k}{\rho\;{f_{k}\left( {{xT_{a}}\  - T_{k} - {\Delta T_{c}}} \right)}}}}} \\{= {{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {\rho\; c{\sum\limits_{k}{f_{k}\left( {{x\left( {T_{a} - T_{k}} \right)} - {\Delta T_{c}}} \right)}}}}} \\{\approx {{\overset{\_}{Q}\left( \overset{\_}{T} \right)} + {\rho\; c{\overset{\_}{f}\left( {{x\left( {T_{a} - \overset{\_}{T}} \right)} - {\Delta T_{c}}} \right)}}}}\end{matrix}$

according to some embodiments (assuming that T_(k)≈T for each zone 206).This yields the aggregate thermal model:

${\rho\; c\overset{\_}{V}\frac{d\overset{\_}{T}}{dt}} = {{{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {\rho\; c{\sum\limits_{k}{f_{k}\left( {{x\left( {T_{a} - T_{k}} \right)} - {\Delta T_{c}}} \right)}}}} \approx {{\overset{\_}{Q}\left( \overset{\_}{T} \right)} + {\rho\; c{\overset{\_}{f}\left( {{x\left( {T_{a} - \overset{\_}{T}} \right)} - {\Delta T_{c}}} \right)}}}}$

according to some embodiments.

The moisture model

$\rho{V_{k}\left( \frac{d\omega_{k}}{dt} \right)}$

can similarly be aggregated to yield an aggregate moisture model:

$\begin{matrix}{{\rho\;\overset{\_}{V}\frac{d\;\overset{\_}{\omega}}{dt}} = {\overset{\_}{w} + {\rho{\sum\limits_{k}{f_{k}\left( {{x\left( {\omega_{a} - \omega_{k}} \right)} - {\Delta\omega_{c}}} \right)}}}}} \\{\approx {\overset{\_}{w} + {\rho\;{\overset{\_}{f}\left( {{x\left( {\omega_{a} - \overset{\_}{\omega}} \right)} - {\Delta\omega_{c}}} \right)}}}}\end{matrix}$

to predict an evolution of volume-averaged humidity, according to someembodiments.

In some embodiments, model manager 416 stores and uses the aggregatequantum concentration model, the aggregate thermal model, and/or theaggregate moisture model described hereinabove. Model manager 416 canpopulate the various parameters of the aggregate models and provide theaggregate models to optimization manager 412 for use in theoptimization.

Referring still to FIG. 4, memory 406 includes optimization manager 412.Optimization manager 412 can be configured to use the models provided bymodel manager 416 and various constraints provided by constraintgenerator 410 to construct an optimization problem for HVAC system 200(e.g., to determine design outputs and/or to determine controlparameters, setpoints, control decisions, etc., for UV lights 306 and/orAHU 304). Optimization manager 412 can construct an optimization problemthat uses the individual or aggregated temperature, humidity, and/orquantum concentration models subject to constraints to minimize energyuse. In some embodiments, decision variables of the optimization problemformulated and solved by optimization manager 412 are the flows f_(k)(or the aggregate f if the optimization problem uses the aggregatemodels), the outdoor air fraction x and the infectious quanta removalfraction λ.

The infectious quanta removal fraction λ is defined as:

λ=λ_(filter)+λ_(UV)

where λ_(filter) is an infectious quanta removal fraction that resultsfrom using filter 308 (e.g., an amount or fraction of infectious quantathat is removed by filter 308), and λ_(UV) is an infectious quantaremoval fraction that results from using UV lights 306 (e.g., an amountor fraction of infectious quanta that is removed by operation of UVlights 306). In some embodiments, λ_(filter) is a design-time constant(e.g., determined based on the chosen filter 308), whereas λ_(UV) is anadjustable or controllable variable that can be determined byoptimization manager 412 by performing the optimization of theoptimization problem. In some embodiments, λ_(UV) is a discretevariable. In some embodiments, λ_(UV) is a continuous variable.

Instantaneous electricity or energy consumption of HVAC system 200 ismodeled using the equation (e.g., an objective function that isminimized):

E=η _(coil) ρf (cΔT _(c) +LΔω _(c))+η_(fan) fΔP+η _(UV)λ_(UV)

where L is a latent heat of water, ΔP is a duct pressure drop, η_(coil)is an efficiency of the cooling coil of AHU 304, η_(fan) is anefficiency of a fan of AHU 304, and η_(UV) is an efficiency of the UVlights 306, according to some embodiments. In some embodiments,optimization manager 412 is configured to store and use the energyconsumption model shown above for formulating and performing theoptimization. In some embodiments, the term η_(coil)ρf(cΔT_(c)+LΔω_(c))is an amount of energy consumed by the cooling coil or heating coil ofthe AHU 304 (e.g., over an optimization time period or time horizon),the term η_(fan) fΔP is an amount of energy consumed by the fan of theAHU 304, and η_(UV)λ_(UV) is the amount of energy consumed by the UVlights 306. In some embodiments, the duct pressure drop ΔP is affectedby or related to a choice of a type of filter 308, where higherefficiency filters 308 (e.g., filters 308 that have a higher value ofη_(filter)) generally resulting in a higher value of the duct pressuredrop ΔP and therefore greater energy consumption. In some embodiments, amore complex model of the energy consumption is used by optimizationmanager 412 to formulate the optimization problem (e.g., a non-linearfan model and a time-varying or temperature-dependent coil efficiencymodel).

In some embodiments, the variables ΔT_(c) and Δω_(c) for the coolingcoil of the AHU 304 are implicit dependent decision variables. In someembodiments, a value of a supply temperature T_(AHU) is selected for theAHU 304 and is used to determine the variables ΔT_(c) and Δω_(c) basedon inlet conditions to the AHU 304 (e.g., based on sensor data obtainedby sensor manager 414). In such an implementation, model manager 416 oroptimization manager 412 may determine that T₀=T_(AHU) and an equationfor ω₀.

Optimization manager 412 can use the models (e.g., the individualmodels, or the aggregated models) provided by model manager 416, andconstraints provided by constraint generator 410 to construct theoptimization problem. Optimization manager 412 may formulate anoptimization problem to minimize energy consumption subject toconstraints on the modeled parameters, ω, and N and additionalconstraints:

$\min\limits_{f_{t},x_{t},\lambda_{t}}$ $\sum\limits_{t}E_{t}$   (EnergyCost) s.t. . . . (Dynamic Models for T_(t), ω_(t), and N_(t)) . . .(Infection Probability Constraint) T_(t) ^(min) ≤ T_(t) ≤ T_(t) ^(max)(Temperature Bounds) ω_(t) ^(min) ≤ ω_(t) ≤ ω_(t) ^(max) (HumidityBounds) x_(t)f_(t) ≥ F_(t) ^(min) (Fresh-Air Ventilation Bound) f_(t)^(min) ≤ f_(t) ≤ f_(t) ^(max) (VAV Flow Bounds) 0 ≤ x_(t) ≤ 1(Outdoor-Air Damper Bounds)where Σ_(t) E_(t) is the summation of instantaneous electricity orenergy consumption of the HVAC system 200 over an optimization timeperiod, subject to the dynamic models for T_(t), ω_(t), and N_(t)(either zone-by-zone individual models, or aggregated models asdescribed above), an infection probability constraint (described ingreater detail below), temperature boundary constraints (T_(t)^(min)≤T_(t)≤T_(t) ^(max), maintaining T_(t) between a minimumtemperature boundary T_(t) ^(min) and a maximum temperature boundaryT_(t) ^(max)), humidity boundary constraints (ω_(t) ^(min)≤ω_(t)≤ω_(t)^(max), maintaining the humidity ω_(t) between a minimum humidityboundary ω_(t) ^(min) and a maximum humidity boundary ω_(t) ^(max)), afresh air ventilation boundary (x_(t)f_(t)≥F_(t) ^(min), maintaining thefresh air ventilation x_(t) f_(t) above or equal to a minimum requiredamount F_(t) ^(min)), a VAV flow boundary (f_(t) ^(min)≤f_(t)≤f_(t)^(max), maintaining the volumetric flow rate f_(t) between a minimumboundary f_(t) ^(min) and a maximum boundary f_(t) ^(max)), and anoutdoor air damper bound/constraint (0≤x_(t)≤1 maintaining the outdoorair fraction x_(t) between 0 and 1). In some embodiments, optimizationmanager 412 is configured to discretize the dynamic models (e.g., theindividual dynamic models or the aggregate dynamic models) using matrixexponentials or approximately using collocation methods.

The boundaries on temperature (T_(t) ^(min)≤T_(t)≤T_(t) ^(max)) andhumidity (ω_(t) ^(min)≤ω_(t)≤ω_(t) ^(max)) can be determined byoptimization manager 412 based on user inputs or derived from comfortrequirements. The temperature and humidity bounds may be enforced byoptimization manager 412 as soft constraints. The remaining bounds(e.g., the fresh-air ventilation bound, the VAV flow bounds, and theoutdoor-air damper bounds) can be applied to input quantities (e.g.,decision variables) by optimization manager 412 as hard constraints forthe optimization. In some embodiments, the fresh-air ventilation boundis enforced by optimization manager 412 to meet the American Society ofHeating, Refrigerating, and Air-Conditioning Engineers (ASHRAE)standards. In some embodiments, the fresh-air ventilation bound isreplaced with a model and corresponding bounds for CO2 concentration.

In some embodiments, the various constraints generated by constraintgenerator 410 or other constraints imposed on the optimization problemcan be implemented as soft constraints, hard constraints, or acombination thereof. Hard constraints may impose rigid boundaries (e.g.,maximum value, minimum value) on one or more variables in theoptimization problem such that any feasible solution to the optimizationproblem must maintain the hard constrained variables within the limitsdefined by the hard constraints. Conversely, soft constraints may beimplemented as penalties that contribute to the value of the objectivefunction (e.g., adding to the objective function if the optimizationproblem seeks to minimize the objective function or subtracting from theobjective function if the optimization problem seeks to maximize theobjective function). Soft constraints may be violated when solving theoptimization problem, but doing so will incur a penalty that affects thevalue of the objective function. Accordingly, soft constraints mayencourage optimization manager 412 to maintain the values of the softconstrained variables within the limits defined by the soft constraintswhenever possible to avoid the penalties, but may allow optimizationmanager 412 to violate the soft constraints when necessary or when doingso would result in a more optimal solution.

In some embodiments, constraint generator 410 may impose softconstraints on the optimization problem by defining large penaltycoefficients (relative to the scale of the other terms in the objectivefunction) so that optimization manager 412 only violates the softconstraints when absolutely necessary. However, it is contemplated thatthe values of the penalty coefficients can be adjusted or tuned (e.g.,by a person or automatically by constraint generator 410) to provide anoptimal tradeoff between maintaining the soft constrained variableswithin limits and the resulting cost (e.g., energy cost, monetary cost)defined by the objective function. One approach which can be used byconstraint generator 410 is to use penalties proportional to amount bywhich the soft constraint is violated (i.e., static penaltycoefficients). For example, a penalty coefficient of 0.1 $/° C.·hr for asoft constrained temperature variable would add a cost of $0.10 to theobjective function for every 1° C. that the temperature variable isoutside the soft constraint limit for every hour of the optimizationperiod. Another approach which can be used by constraint generator 410is to use variable or progressive penalty coefficients that depend onthe amount by which the soft constraint is violated. For example, avariable or progressive penalty coefficient could define a penalty costof 0.1 $/° C.·hr for the first 1° C. by which a soft constrainedtemperature variable is outside the defined limit, but a relativelyhigher penalty cost of 1.0 $/° C.·hr for any violations of the softconstrained temperature limit outside the first 1° C.

Another approach which can be used by constraint generator 410 is toprovide a “constraint violation budget” for one or more of theconstrained variables. The constraint violation budget may define atotal (e.g., cumulative) amount by which a constrained variable isallowed to violate a defined constraint limit within a given timeperiod. For example a constraint violation budget for a constrainedtemperature variable may define 30° C.·hr (or any other value) as thecumulative amount by which the constrained temperature variable isallowed to violate the temperature limit within a given time period(e.g., a day, a week, a month, etc.). This would allow the temperatureto violate the temperature constraint by 30° C. for a single hour, 1° C.for each of 30 separate hours, 0.1° C. for each of 300 separate hours,10° C. for one hour and 1° C. for each of 20 separate hours, or anyother distribution of the 30° C.·hr amount across the hours of the giventime period, provided that the cumulative temperature constraintviolation sums to 30° C.·hr or less. As long as the cumulativeconstraint violation amount is within (e.g., less than or equal to) theconstraint violation budget, constraint generator 410 may not add apenalty to the objective function or subtract a penalty from theobjective function. However, any further violations of the constraintthat exceed the constraint violation budget may trigger a penalty. Thepenalty can be defined using static penalty coefficients orvariable/progressive penalty coefficients as discussed above.

The infection probability constraint (described in greater detail below)is linear, according to some embodiments. In some embodiments, twosources of nonlinearity in the optimization problem are the dynamicmodels and a calculation of the coil humidity reduction Δω_(c). In someembodiments, the optimization problem can be solved using nonlinearprogramming techniques provided sufficient bounds are applied to theinput variables.

Infection Probability Constraint

Referring still to FIG. 4, memory 406 is shown to include a constraintgenerator 410. Constraint generator 410 can be configured to generatethe infection probability constraint, and provide the infectionprobability constraint to optimization manager 412. In some embodiments,constraint generator 410 is configured to also generate the temperaturebounds, the humidity bounds, the fresh-air ventilation bound, the VAVflow bounds, and the outdoor-air damper bounds and provide these boundsto optimization manager 412 for performing the optimization.

For the infection probability constraint, the dynamic extension of theWells-Riley equation implies that there should be an average constraintover a time interval during which an individual is in the building. Anindividual i's probability of infection P_(i,[0, T]) over a timeinterval [0, T] is given by:

${P_{i,{\lbrack{0,T}\rbrack}} = {1 - {\exp\left( {{- p}\Delta{\sum\limits_{t}{\delta_{it}N_{t}}}} \right)}}},{\delta_{it} = \left\{ \begin{matrix}1 & {{if}\mspace{14mu} i\mspace{14mu}{present}\mspace{14mu}{at}\mspace{14mu}{time}\mspace{14mu} t} \\0 & {else}\end{matrix} \right.}$

according to some embodiments. Assuming that the individual'sprobability of infection P_(i,[0, T]) is a known value, an upper boundP^(max) can be chosen for P_(i,[0, T]) and can be implemented as alinear constraint:

${\sum\limits_{t}{\delta_{it}N_{t}}} \leq {{- \frac{1}{p\Delta}}{\log\left( {1 - P^{\max}} \right)}}$

according to some embodiments. In some embodiments, the variable δ_(it)may be different for each individual in the building 10 but can beapproximated as described herein.

The above linear constraint is an average constraint that givesoptimization manager 412 (e.g., an optimizer) a maximum amount offlexibility since the average constraint may allow a higherconcentration of infectious quanta during certain times of the day(e.g., when extra fresh-air ventilation is expensive due to outdoorambient conditions) as long as the higher concentrations are balanced bylower concentrations of the infectious quanta during other times of theday. However, the δ_(it) sequence may be different for each individualin the building 10. For purposes of the example described herein it isassumed that generally each individual is present a total of 8 hours(e.g., if the building 10 is an office building). However, the estimatedamount of time the individual is within the building can be adjusted orset to other values for other types of buildings. For example, when thesystems and methods described herein are implemented in a restaurant orstore, the amount of time the individual is assumed to be present in thebuilding can be set to an average or estimated amount of time requiredto complete the corresponding activities (e.g., eating a meal, shopping,etc.). While an occupancy time of the building by each individual may bereasonably known, the times that the individual is present in thebuilding may vary (e.g., the individual may be present from 7 AM to 3PM, 9 AM to 5 PM, etc.). Therefore, to ensure that the constraint issatisfied for all possible δ_(it) sequences, the constraint may berequired to be satisfied when summing over 8 hours of the day that havea highest concentration.

This constraint is represented using linear constraints as:

${{{{M\eta} + {\sum\limits_{t}\mu_{t}}} \leq {{- \frac{1}{p\Delta}}{\log\left( {1 - P^{\max}} \right)}}}{\mu_{t} + \eta}} \geq {N_{t}\mspace{20mu}{\forall t}}$

where η and μ_(t) are new auxiliary variables in the optimizationproblem, and M is a number of discrete timesteps corresponding to 8hours (or any other amount of time that an individual is expected tooccupy building 10 or one of building zones 206). This formulation maywork since η is set to an Mth highest value of N_(t) and each of theμ_(t) satisfy μ_(t)=max(N_(t)η, 0). Advantageously, this implementationof the infection probability constraint can be generated by constraintgenerator 410 and provided to optimization manager 412 for use in theoptimization problem when controller 310 is implemented to performcontrol decisions for HVAC system 200 (e.g., when controller 310operates in an on-line mode).

An alternative implementation of the infection probability constraint isshown below that uses a pointwise constraint:

${N_{t} \leq N_{t}^{\max}} = {{- \frac{1}{Mp\Delta}}{\log\left( {1 - P^{\max}} \right)}}$

where N_(t) is constrained to be less than or equal to N_(t) ^(max) fora maximum infection probability value P^(max). In some embodiments, thepointwise constraint shown above is generated by constraint generator410 for when optimization manager 412 is used in an off-line or designimplementation. In some embodiments, the pointwise constraint shownabove, if satisfied in all zones 206, ensures that any individual willmeet the infection probability constraint. Such a constraint maysacrifice flexibility compared to the other implementation of theinfection probability constraint described herein, but translates to asimple box constraint similar to the other bounds in the optimizationproblem, thereby facilitating a simpler optimization process.

In some embodiments, the maximum allowable or desirable infectionprobability p^(max) is a predetermined value that is used by constraintgenerator 410 to generate the infection probability constraintsdescribed herein. In some embodiments, constraint generator 410 isconfigured to receive the maximum allowable or desirable infectionprobability p^(max) from a user as a user input. In some embodiments,the maximum allowable or desirable infection probability P^(max) is anadjustable parameter that can be set by a user or automaticallygenerated based on the type of infection, time of year, type or use ofthe building, or any of a variety of other factors. For example, somebuildings (e.g., hospitals) may be more sensitive to preventing diseasespread than other types of buildings and may use lower values ofP^(max). Similarly, some types of diseases may be more serious orlife-threatening than others and therefore the value of P^(max) can beset to relatively lower values as the severity of the disease increases.In some embodiments, the value of P^(max) can be adjusted by a user andthe systems and methods described herein can run a plurality ofsimulations or optimizations for a variety of different values ofP^(max) to determine the impact on cost and disease spread. A user canselect the desired value of P^(max) in view of the estimated cost andimpact on disease spread using the results of the simulations oroptimizations.

Model Enhancements

Referring still to FIG. 4, optimization manager 412, constraintgenerator 410, and/or model manager 416 can implement various modelenhancements in the optimization. In some embodiments, optimizationmanager 412 is configured to add a decision variable for auxiliary(e.g., controlled) heating (e.g., via baseboard heat or VAV reheatcoils). In some embodiments, an effect of the auxiliary heating isincluded in the dynamic model of temperature similar to the disturbanceheat load Q_(k)(⋅). Similar to the other decision variables, theauxiliary heating decision variable may be subject to bounds (e.g., withboth set to zero during cooling season to disable auxiliary heating)that are generated by constraint generator 410 and used by optimizationmanager 412 in the optimization problem formulation and solving. In someembodiments, the auxiliary heating also results in optimization manager412 including another term for associated energy consumption in theenergy consumption equation (shown above) that is minimized.

In some embodiments, certain regions or areas may have variableelectricity prices and/or peak demand charges. In some embodiments, theobjective function (e.g., the energy consumption equation) can beaugmented by optimization manager 412 to account for such coststructures. For example, the existing energy consumption E_(t) that isminimized by optimization manager 412 may be multiplied by acorresponding electricity price P_(t). A peak demand charge may requirethe use of an additional parameter e_(t) that represents a base electricload of building 10 (e.g., for non-HVAC purposes). Optimization manager412 can include such cost structures and may minimize overall costassociated with electricity consumption rather than merely minimizingelectrical consumption. In some embodiments, optimization manager 412accounts for revenue which can be generated by participating inincentive based demand response (IBDR) programs, frequency regulation(FR) programs, economic load demand response (ELDR) programs, or othersources of revenue when generating the objective function. In someembodiments, optimization manager 412 accounts for the time value ofmoney by discounting future costs or future gains to their net presentvalue. These and other factors which can be considered by optimizationmanager 412 are described in detail in U.S. Pat. No. 10,359,748 grantedJul. 23, 2019, U.S. Patent Application Publication No. 2019/0347622published Nov. 14, 2019, and U.S. Patent Application Publication No.2018/0357577 published Dec. 13, 2018, each of which is incorporated byreference herein in its entirety.

In some embodiments, certain locations have time-varying electricitypricing, and therefore there exists a potential to significantly reducecooling costs by using a solid mass of building 10 for thermal energystorage. In some embodiments, controller 310 can operate to pre-cool thesolid mass of building 10 when electricity is cheap so that the solidmass can later provide passive cooling later in the day when electricityis less expensive. In some embodiments, optimization manager 412 and/ormodel manager 416 are configured to model this effect using a modelaugmentation by adding a new variable T_(k) ^(m) to represent the solidmass of the zone 206 evolving as:

${\rho c_{m}V_{k}^{m}\frac{dT_{k}^{m}}{dt}} = {h_{k}^{m}\left( {T_{k} - T_{k}^{m}} \right)}$

with a corresponding term:

${\rho cV_{k}\frac{dT_{k}}{dt}} = {\text{…} + {h_{k}^{m}\left( {T_{k}^{m} - T_{k}} \right)}}$

added to the air temperature model (shown above). This quantity can alsobe aggregated by model manager 416 to an average value T ^(m) similar toT.

For some diseases, infectious particles may naturally become deactivatedor otherwise removed from the air over time. To consider these effects,controller 310 can add a proportional decay term to the infectiousquanta model (in addition to the other terms of the infectious quantamodel discussed above). An example is shown in the following equation:

${V\frac{dN}{dt}} = {\text{…} - {V\beta N}}$

where β represents the natural decay rate (in s⁻¹) of the infectiousspecies and the ellipsis represents the other terms of the infectiousquanta model as discussed above. Because thenatural decay subtracts from the total amount of infectious particles,the natural decay term is subtracted from the other terms in theinfectious quanta model. For example, if a given infectious agent has ahalf-life t_(1/2) of one hour (i.e., t_(1/2)=1 hr=3600 s), then thecorresponding decay rate is given by:

$\beta = {\frac{\ln(2)}{t_{1/2}} \approx {{1.9}25 \times 10^{- 4}s^{- 1}}}$

This extra term can ensure that infectious particle concentrations donot accumulate indefinitely over extremely long periods of time.

Off-Line Optimization

Referring particularly to FIG. 5, controller 310 can be configured foruse as a design or planning tool for determining various designparameters of HVAC system 300 (e.g., for determining a size of filter308, UV lights 306, etc.). In some embodiments, controller 310implemented as a design tool, a planning tool, a recommendation tool,etc., (e.g., in an off-line mode) functions similarly to controller 310implemented as a real-time control device (e.g., in an on-line mode).However, model manager 416, constraint generator 410, and optimizationmanager 412 may receive required sensor input data (i.e., modelpopulation data) from a simulation database 424. Simulation database 424can store values of the various parameters of the constraints orboundaries, the dynamic models, or typical energy consumption costs oroperational parameters for energy-consuming devices of the HVAC system200. In some embodiments, simulation database 424 also stores predictedor historical values as obtained from sensors of HVAC system 200. Forexample, simulation database 424 can store typical ambient temperature,humidity, etc., conditions for use in performing the off-linesimulation.

When controller 310 is configured for use as the design tool (shown inFIG. 5), controller 310 may receive user inputs from user input device420. The user inputs may be initial inputs for various constraints(e.g., a maximum value of the probability of infection for thesimulation) or various required input parameters. The user can alsoprovide simulation data for simulation database 424 used to populate themodels or constraints, etc. Controller 310 can output suggestions ofwhether to use a particular piece of equipment (e.g., whether or not touse or install UV lights 306), whether to use AHU 304 to draw outsideair, etc., or other factors to minimize cost (e.g., to optimize theobjective function, minimize energy consumption, minimize energyconsumption monetary cost, etc.) and to meet disinfection goals (e.g.,to provide a desired level of infection probability). In someembodiments, controller 310 may provide different recommendations orsuggestions based on a location of building 10. In some embodiments, therecommendations notify the user regarding what equipment is needed tokeep the infection probability of zones 206 within the threshold whilenot increasing energy cost or carbon footprint.

Compared to the on-line optimization (described in greater detailbelow), the optimization problem formulated by optimization manager 412for the off-line implementation includes an additional constraint on theinfectious quanta concentration (as described in greater detail above).In some embodiments, the infectious quanta concentration can becontrolled or adjusted by (a) changing the airflow into each zone 206(e.g., adjusting f_(i)), (b) changing the fresh-air intake fraction(e.g., adjusting x), or (c) destroying infectious particles in the AHU304 via filtration or UV light (e.g., adjustingλ).

It should be noted that the first and second control or adjustments(e.g., (a) and (b)) may also affect temperature and humidity of thezones 206 of building 10. However, the third control option (c) (e.g.,adjusting the infectious quanta concentration through filtration and/oroperation of UV lights) is independent of the temperature and humidityof the zones 206 of building 10 (e.g., does not affect the temperatureor humidity of zones 206 of building 10). In some embodiments,optimization manager 412 may determine results that rely heavily orcompletely on maintaining the infectious quanta concentration below itscorresponding threshold or bound through operation of filter 308 and/orUV lights 306. However, there may be sufficient flexibility in thetemperature and humidity of building zone 206 so that optimizationmanager 412 can determine adjustments to (a), (b), and (c)simultaneously to achieve lowest or minimal operating costs (e.g.,energy consumption). Additionally, since purchasing filters 308 and/orUV lights 306 may incur significant capital costs (e.g., to purchasesuch devices), controller 310 may perform the optimization as asimulation to determine if purchasing filters 308 and/or UV lights 306is cost effective.

When controller 310 is configured as the design tool shown in FIG. 5,controller 310 may provide an estimate of a total cost (both capitalcosts and operating costs) to achieve a desired level of infectioncontrol (e.g., to maintain the infection probability below or at adesired amount). The purpose is to run a series of independentsimulations, assuming different equipment configurations (e.g., asstored and provided by simulation database 424) and for differentinfection probability constraints given typical climate and occupancydata (e.g., as stored and provided by simulation database 424). In someembodiments, the different equipment configurations include scenarioswhen filters 308 and/or UV lights 306 are installed in the HVAC system200, or when filters 308 and/or UV lights 306 are not installed in theHVAC system 200.

After performing the simulation for different equipment configurationscenarios and/or different infection probability constraints, controller310 can perform a cost benefit analysis based on global design decisions(e.g., whether or not to install UV lights 306 and/or filters 308). Thecost benefit analysis may be performed by results manager 418 and thecost benefit analysis results can be output as display data to abuilding manager via display device 422. These results may aid thebuilding manager or a building designer in assessing potential optionsfor infection control of building 10 (as shown in FIG. 8).

Referring particularly to FIGS. 5 and 8, graph 800 illustrates apotential output of results manager 418 that can be displayed by displaydevice 422. Graph 800 illustrates relative cost (the Y-axis) withrespect to infection probability (the X-axis) for a case when bothfiltration and UV lights are used for infection control (represented byseries 808), a case when filtration is used for infection controlwithout using UV lights (represented by series 802), a case when UVlights are used for infection control without using filtration(represented by series 806), and a case when neither UV lights andfiltration are used for infection control (represented by series 804).In some embodiments, each of the cases illustrated by series 802-808assume that fresh-air intake is used to control infection probability.Data associated with graph 800 can be output by results manager 418 sothat graph 800 can be generated and displayed on display device 422.

In some embodiments, the off-line optimization performed by optimizationmanager 412 is faster or more computationally efficient than the on-lineoptimization performed by optimization manager 412. In some embodiments,the simulation is performed using conventional rule-based control ratherthan a model-predictive control scheme used for the on-lineoptimization. Additionally, the simulation may be performed over shortertime horizons than when the optimization is performed in the on-linemode to facilitate simulation of a wide variety of design conditions.

In some embodiments, optimization manager 412 is configured to use theaggregate dynamic models as generated, populated, and provided by modelmanager 416 for the off-line optimization (e.g., the designoptimization). When optimization manager 412 uses the aggregate dynamicmodels, this implies that there are three decision variables of theoptimization: f, x, and λ. The variable λ can include two positions ateach timestep (e.g., corresponding to the UV lights 306 being on or theUV lights 306 being off). A reasonable grid size of f and x may be 100.Accordingly, this leads to 100×100×2=20,000 possible combinations ofcontrol decisions at each step, which is computationally manageable.Therefore, optimization manager 412 can select values of the variablesf, x, and λ via a one-step restriction of the optimization problem bysimply evaluating all possible sets of control inputs and selecting theset of control inputs that achieves a lowest cost.

If additional variables are used, such as an auxiliary heating variable,this may increase the dimensionality of the optimization problem.However, optimization manager 412 can select a coarser grid (e.g., 5 to10 choices) for the additional variable.

In some embodiments, optimization manager 412 is configured to solve anumber of one-step optimization problems (e.g., formulate differentoptimization problems for different sets of the control variables andsolve the optimization problem over a single timestep) in a trainingperiod, and then train a function approximator (e.g., a neural network)to recreate a mapping. This can improve an efficiency of theoptimization. In some embodiments, optimization manager 412 isconfigured to apply a direct policy optimization to the dynamic modelsin order to directly learn a control law using multiple paralleloptimization problems.

In some embodiments, when controller 310 functions as the design toolshown in FIG. 5, there are two design variables. The first designvariable is whether it is cost effective or desirable to purchase andinstall UV lights 306, and the second design variable is whether it iscost effective or desirable to purchase and install filters 308 (e.g.,advanced filtration devices).

In some embodiments, optimization manager 412 is configured to perform avariety of simulations subject to different simulation variables foreach simulation month. These simulation variables can be separated intoa design decision category and a random parameter category. The designdecision category includes variables whose values are chosen by systemdesigners, according to some embodiments. The random parameters categoryincludes variables whose values are generated by external (e.g., random)processes.

The design decision category can include a first variable of whether toactivate UV lights 306. The first variable may have two values (e.g., afirst value for when UV lights 306 are activated and a second value forwhen UV lights 306 are deactivated). The design decision category caninclude a second decision variable of which of a variety ofhigh-efficiency filters to use, if any. The second variable may have anynumber of values that the building manager wishes to simulate (e.g., 5)and can be provided via user input device 420. The design decisionscategory can also include a third variable of what value should be usedfor the infection probability constraint (as provided by constraintgenerator 410 and used in the optimization problem by optimizationmanager 412). In some embodiments, various values of the third variableare also provided by the user input device 420. In some embodiments,various values of the third variable are predetermined or stored insimulation database 424 and provided to optimization manager 412 for usein the simulation. The third variable may have any number of values asdesired by the user (e.g., 3 values).

The random parameters category can include an ambient weather and zoneoccupancy variable and a number of infected individuals that are presentin building 10 variable. In some embodiments, the ambient weather andzone occupancy variable can have approximately 10 different values. Insome embodiments, the number of infected individuals present can haveapproximately 5 different values.

In order to determine a lowest cost for a given month, optimizationmanager 412 can aggregate the variables in the random parameterscategory (e.g., average) and then perform an optimization to minimizethe energy consumption or cost over feasible values of the variables ofthe design decisions category. In some embodiments, some of thedesign-decision scenarios are restricted by a choice of global designdecisions. For example, for optimization manager 412 to calculatemonthly operating costs assuming UV lights 306 are chosen to beinstalled but not filtration, optimization manager 412 may determinethat a lowest cost scenario across all scenarios is with no filtrationbut with the UV lights 306 enabled or disabled. While this may beunusual (e.g., for the UV lights 306 to be disabled) even though the UVlights 306 are installed, various conditions (e.g., such as weather) maymake this the most cost effective solution.

In some embodiments, simulation logic performed by optimization manager412 may be performed in a Tensorflow (e.g., as operated by a laptopcomputer, or any other sufficiently computationally powerful processingdevice). In order to perform 1,500 simulation scenarios for each month,or 18,000 for an entire year, with a timestep of 15 minutes, thisimplies a total of approximately 52 million timesteps of scenarios for agiven simulation year.

In some embodiments, optimization manager 412 requires varioussimulation data in order to perform the off-line simulation (e.g., todetermine the design parameters). In some embodiments, the simulationdata is stored in simulation database 424 and provided to any ofconstraint generator 410, model manager 416, and/or optimization manager412 as required to perform their respective functions. The simulationdata stored in simulation database 424 can include heat-transferparameters for each zone 206, thermal and moisture loads for each zone206, coil model parameters of the AHU 304, fan model parameters of theAHU 304, external temperature, humidity, and solar data, filtrationefficiency, pressure drop, and cost versus types of the filter 308,disinfection fraction and energy consumption of the UV lights 306,installation costs for the UV lights 306 and the filter 308, typicalbreathing rate p, a number of infected individuals Ī in building zones206, and disease quanta generation q values for various diseases. Insome embodiments, the heat-transfer parameters for each zone 206 may beobtained by simulation database 424 from previous simulations or fromuser input device 420. In some embodiments, the thermal and moistureloads for each zone 206 are estimated based on an occupancy of the zones206 and ASHRAE guidelines. After this simulation data is obtained insimulation database 424, controller 310 may perform the simulation(e.g., the off-line optimization) as described herein.

It should be understood that as used throughout this disclosure, theterm “optimization” may signify a temporal optimization (e.g., across atime horizon) or a static optimization (e.g., at a particular moment intime, an instantaneous optimization). In some embodiments, optimizationmanager 412 is configured to either run multiple optimizations fordifferent equipment selections, or is configured to treat equipmentconfigurations as decision variables and perform a single optimizationto determine optimal equipment configurations.

It should also be understood that the term “design” as used throughoutthis disclosure (e.g., “design data” and/or “design tool”) may includeequipment recommendations (e.g., recommendations to purchase particularequipment or a particular type of equipment such as a particular filter)and/or operational recommendations for HVAC system 200. In other words,“design data” as used herein may refer to any information, metrics,operational data, guidance, suggestion, etc., for selecting equipment,an operating strategy, or any other options to improve financial metricsor other control objectives (e.g., comfort and/or infectionprobability).

For example, controller 310 as described in detail herein with referenceto FIG. 5 may be configured to provide recommendations of specificmodels to purchase. In some embodiments, controller 310 is configured tocommunicate with an equipment performance database to provideproduct-specific selections. For example, controller 310 can search thedatabase for equipment that has particular specifications as determinedor selected by the optimization. In some embodiments, controller 310 mayalso provide recommended or suggested control algorithms (e.g., modelpredictive control) as the design data. In some embodiments, controller310 may provide a recommendation or suggestion of a general type ofequipment or a general equipment configuration without specifying aparticular model. In some embodiments, controller 310 may also recommenda specific filter or a specific filter rating. For example, optimizationmanager 412 can perform multiple optimizations with different filterratings and select the filter ratings associated with an optimal result.

On-Line Optimization

Referring again to FIG. 4, controller 310 can be implemented as anon-line controller that is configured to determine optimal control forthe equipment of building 10. Specifically, controller 310 may determineoptimal operation for UV lights 306 and AHU 304 to minimize energyconsumption after UV lights 306 and/or filter 308 are installed and HVACsystem 200 is operational. When controller 310 is configured as anon-line controller, controller 310 may function similarly to controller310 as configured for off-line optimization and described in greaterdetail above with reference to FIG. 5. However, controller 310 candetermine optimal control decisions for the particular equipmentconfiguration of building 10.

In some embodiments, optimization manager 412 is configured to performmodel predictive control similar to the techniques described in U.S.patent application Ser. No. 15/473,496, filed Mar. 29, 2017, the entiredisclosure of which is incorporated by reference herein.

While optimization manager 412 can construct and optimize theoptimization problem described in greater detail above, and shown below,using MPC techniques, a major difference is that optimization manager412 performs the optimization with an infectious quanta concentrationmodel as described in greater detail above.

$\min\limits_{f_{t},x_{t},\lambda_{t}}$ $\sum\limits_{t}E_{t}$   (EnergyCost) s.t. . . . (Dynamic Models for T_(t), ω_(t), and N_(t)) . . .(Infection Probability Constraint) T_(t) ^(min) ≤ T_(t) ≤ T_(t) ^(max)(Temperature Bounds) ω_(t) ^(min) ≤ ω_(t) ≤ ω_(t) ^(max) (HumidityBounds) x_(t)f_(t) ≥ F_(t) ^(min) (Fresh-Air Ventilation Bound) f_(t)^(min) ≤ f_(t) ≤ f_(t) ^(max) (VAV Flow Bounds) 0 ≤ x_(t) ≤ 1(Outdoor-Air Damper Bounds)

Therefore, the resulting optimization problem has additional constraintson this new variable (the infectious quanta concentration) but also newflexibility by determined decisions for activating UV lights 306. Insome embodiments, the optimization performed by optimization manager 412can balance, in real time, a tradeoff between takin gin additionaloutdoor air (which generally incurs a cooling energy penalty) andactivating the UV lights 306 (which requires electricity consumption).Additionally, the addition of infectious agent control can also provideadditional room optimization of HVAC system 200 during a heating season(e.g., during winter). Without considering infectious quantaconcentrations, solutions generally lead to a minimum outdoor airflowbelow a certain break-even temperature, below which heating is requiredthroughout building 10. However, since the optimization problemformulated by optimization manager 412 can determine to increase outdoorair intake, this can provide an additional benefit of disinfection.

For purposes of real-time or on-line optimization, the HVAC system 200can be modeled on a zone-by-zone basis due to zones 206 each havingseparate temperature controllers and VAV boxes. In some embodiments,zone-by-zone temperature measurements are obtained by controller 310from zone sensors 312 (e.g., a collection of temperature, humidity, CO2,air quality, etc., sensors that are positioned at each of the multiplezones 206). In some embodiments, optimization manager 412 is configuredto use zone-level temperature models but aggregate humidity andinfectious quanta models for on-line optimization. Advantageously, thiscan reduce a necessary modeling effort and a number of decisionvariables in the optimization problem. In some embodiments, if the AHU304 serves an excessive number of zones 206, the zone-level thermalmodeling may be too computationally challenging so optimization manager412 can use aggregate temperature models.

After optimization manager 412 has selected whether to use individual oraggregate models (or some combination thereof), optimization manager 412can implement a constraint in the form:

$\frac{dx}{dt} = {{{f\left( {{x(t)},{u(t)},{p(t)}} \right)}\mspace{14mu}{for}\mspace{14mu}{all}\mspace{14mu} t} \in \left\lbrack {0,T} \right\rbrack}$

given a horizon t, where u(t) is a decision, control, or adjustablevariable, and p(t) are time-varying parameters (the values of which areforecasted ahead of time). In some embodiments, optimization manager 412is configured to implement such a constraint by discretizing the u(t)and p(t) signals into piecewise-constant values u_(n) and p_(n) wherethe discrete index n represents the time interval t ∈[nΔ, (n+1)Δ] for afixed sample time Δ. Optimization manager 412 may then transform theconstraint to:

$\frac{dx}{dt} = {{{f\left( {{x(t)},u_{j},p_{j}} \right)}\mspace{14mu}{for}\mspace{14mu}{all}{\;\mspace{11mu}}t} \in {\left\lbrack {{n\;\Delta},{\left( {n + 1} \right)\Delta}} \right\rbrack\mspace{14mu}{and}}}$n ∈ {0, …  , N − 1}

where N=T/Δ the total number of timesteps. In some embodiments,optimization manager 412 is configured to evaluate this constraint usingadvanced quadrature techniques. For example, optimization manager 412may transform the constraint to:

x _(n+1) =F(x _(n) , u _(n) , p _(n))

where x(t) is discretized to x_(n) and F(⋅) represents a numericalquadrature routine. In some embodiments, if the models provided by modelmanager 416 are sufficiently simple, optimization manager 412 can derivean analytical expression for F(⋅) to perform this calculation directly.

In some embodiments, optimization manager 412 uses an approximatemidpoint method to derive the analytical expression:

$x_{n + 1} = {x_{k} + {{f\left( {\frac{x_{n + 1} + x_{n}}{2},\ u_{n},p_{n}} \right)}\Delta}}$

where the ordinary differential equation f (⋅) is evaluated at amidpoint of the time interval.

In some embodiments, optimization manager 412 is configured torepeatedly solve the optimization problem at regular intervals (e.g.,every hour) to revise an optimized sequence of inputs for control signalgenerator 408. However, since the optimization is nonlinear andnonconvex, it may be advantageous to decrease a frequency at which theoptimization problem is solved to provide additional time to retryfailed solutions.

In some embodiments, optimization manager 412 uses a daily advisorycapacity. For example, optimization manager 412 may construct and solvethe optimization problem once per day (e.g., in the morning) todetermine optimal damper positions (e.g., of AHU 304), UV utilizations(e.g., operation of UV lights 306), and zone-level airflows. Using theresults of this optimization, optimization manager 412 may be configuredto pre-schedule time-varying upper and lower bounds on the variousvariables of the optimized solution, but with a range above and below sothat optimization manager 412 can have sufficient flexibility to rejectlocal disturbances. In some embodiments, regulatory control systems ofHVAC system 200 are maintained but may saturate at new tighter boundsobtained from the optimization problem. However, optimization manager412 may be configured to re-optimize during a middle of the day ifambient sensor data from ambient sensors 314 (e.g., ambient temperature,outdoor temperature, outdoor humidity, etc.) and/or weather forecastsand/or occupancy forecasts indicate that the optimization should bere-performed (e.g., if the weather forecasts are incorrect or change).

In some embodiments, optimization manager 412 is configured to reduce anamount of optimization by training a neural network based on results ofmultiple offline optimal solutions (e.g., determined by controller 310when performing off-line optimizations). In some embodiments, the neuralnetwork is trained to learn a mapping between initial states anddisturbance forecasts to optimal control decisions. The neural networkcan be used in the online implementation of controller 310 as asubstitute for solving the optimization problem. One advantage of usinga neural network is that the neural network evaluation is faster thanperforming an optimization problem, and the neural network is unlikelyto suggest poor-quality local optima (provided such solutions areexcluded from the training data). The neural network may, however,return nonsensical values for disturbance sequences. However, thisdownside may be mitigated by configuring controller 310 to use a hybridtrust-region strategy in which optimization manager 412 solves theoptimization problem via direct optimization at a beginning of the day,and then for the remainder of the day, controller 310 usesneural-network suggestions if they are within a predefined trust regionof the optimal solution. If a neural-network suggestion is outside ofthe predefined trust region, optimization manager 412 may use a previousoptimal solution that is within the predefined trust region.

In some embodiments, the optimization problem is formulated byoptimization manager 412 assuming the zone-level VAV flows f_(k) are thedecision variables. In some systems, however, a main interface betweencontroller 310 and equipment of HVAC system 200 is temperature setpointsthat are sent to zone-level thermostats. In some embodiments,optimization manager 412 and control signal generator 408 are configuredto shift a predicted optimal temperature sequence backward by one timeinterval and then pass these values (e.g., results of the optimization)as the temperature setpoint. For example, if the forecasts over-estimatehead loads in a particular zone 206, then a VAV damper for that zonewill deliver less airflow to the zone 206, since less cooling isrequired to maintain a desired temperature.

When optimization manager 412 uses the constraint on infectious quantaconcentration, controller 310 can now use the zone-level airflow tocontrol two variables, while the local controllers are only aware ofone. Therefore, in a hypothetical scenario, the reduced airflow mayresult in a violation of the constraint on infection probability. Insome embodiments, optimization manager 412 and/or control signalgenerator 408 are configured to maintain a higher flow rate at the VAVeven though the resulting temperature may be lower than predicted. Toaddress this situation, optimization manager 412 may use the minimum andmaximum bounds on the zone-level VAV dampers, specifically setting themto a more narrow range so that the VAV dampers are forced to deliver (atleast approximately) an optimized level of air circulation. In someembodiments, to meet the infectious quanta concentration, the relevantbound is the lower flow limit (as any higher flow will still satisfy theconstraint, albeit at higher energy cost). In some embodiments, asuitable strategy is to set the VAV minimum position at the level thatdelivers 75% to 90% of the optimized flow. In some embodiments, a VAVcontroller is free to dip slightly below the optimized level whenoptimization manager 412 over-estimates heat loads, while also havingthe full flexibility to increase flow as necessary when optimizationmanager 412 under-estimates heat loads. In the former case, optimizationmanager 412 may slightly violate the infectious quanta constraint (whichcould potentially be mitigated via rule-based logic to activate UVlights 306 if flow drops below planned levels), while in the lattercase, the optimal solution still satisfies the constraint on infectiousquanta. Thus, optimization manager 412 can achieve both control goalswithout significant disruption to the low-level regulatory controlsalready in place.

On-Line Optimization Process

Referring particularly to FIG. 6, a process 600 for performing anon-line optimization to minimize energy consumption and satisfy aninfection probability constraint in a building is shown, according tosome embodiments. Process 600 can be performed by controller 310 whencontroller 310 is configured to perform an on-line optimization. In someembodiments, process 600 is performed in real time for HVAC system 200to determine optimal control of AHU 304 and/or UV lights 306. Process600 can be performed for an HVAC system that includes UV lights 306configured to provide disinfection for supply air that is provided toone or more zones 206 of a building 10, filter 308 that filters an airoutput of an AHU, and/or an AHU (e.g., AHU 304). Process 600 can also beperformed for HVAC systems that do not include filter 308 and/or UVlights 306.

Process 600 includes determining a temperature model for each ofmultiple zones to predict a temperature of a corresponding zone based onone or more conditions or parameters of the corresponding zone (step602), according to some embodiments. The temperature model can begenerated or determined by model manager 416 for use in an optimizationproblem. In some embodiments, the temperature model is:

${\rho c{V_{k}\left( \frac{dT_{k}}{dt} \right)}} = {{\rho c{f_{k}\left( {T_{0} - T_{k}} \right)}} + {Q_{k}\left( T_{k} \right)}}$

where ρ is a mass density of air, c is a heat capacity of air, V_(k) isa volume of the kth zone, f_(k) is a volumetric flow of air into the kthzone, T₀ is the temperature of air output by the AHU, T_(k) is thetemperature of the kth zone, and Q_(k) is the heat load on the kth zone.Step 602 can be performed by model manager 416 as described in greaterdetail above with reference to FIGS. 4-5.

Process 600 includes determining a humidity model for each of themultiple zones to predict a humidity of the corresponding zone based onone or more conditions or parameters of the corresponding zone (step604), according to some embodiments. Step 604 can be similar to step 602but for the humidity model instead of the temperature model. In someembodiments, the humidity model is:

${\rho{V_{k}\left( \frac{d\omega_{k}}{dt} \right)}} = {{\rho{f\left( {\omega_{0} - T_{0}} \right)}} + w_{k}}$

for a kth zone 206. In some embodiments, step 604 is performed by modelmanager 416 as described in greater detail above with reference to FIGS.4-5.

Process 600 incudes determining an infectious quanta concentration modelfor each of the multiple zones to predict an infectious quanta of thecorresponding zone based on one or more conditions or parameters of thecorresponding zone (step 606), according to some embodiments. In someembodiments, the infectious quanta concentration model is similar to thehumidity model of step 604 or the temperature model of step 602. Theinfectious quanta concentration model can be:

${V_{k}\left( \frac{dN_{k}}{dt} \right)} = {{f_{k}\left( {N_{0} - N_{k}} \right)} + {I_{k}q}}$

according to some embodiments. In some embodiments, step 606 isperformed by model manager 416.

Process 600 includes determining an aggregated temperature model, anaggregated humidity model, an aggregated infectious quanta model, anaggregated thermal model, and an aggregated moisture model (step 608),according to some embodiments. In some embodiments, step 608 isoptional. Step 608 can include generating or determining each of theaggregated models by determining a volume-average across zones 206. Theaggregate infectious quanta model is:

${\overset{\_}{V}\frac{d\;\overset{\_}{N}}{dt}} = {{{\overset{\_}{I}\; q} - {\left( {\lambda + x - {\lambda x}} \right){\sum\limits_{k}{f_{k}N_{k}}}}} \approx {{\overset{\_}{I}\; q} - {\left( {\lambda + x - {\lambda x}} \right)\overset{\_}{f}\;\overset{\_}{N}}}}$

according to some embodiments. The aggregated thermal model is:

${{\rho c}\overset{\_}{V}\frac{d\;\overset{\_}{T}}{dt}} = {{{\sum\limits_{k}{Q_{k}\left( T_{k} \right)}} + {\rho c{\sum\limits_{k}{f_{k}\left( {{x\left( {T_{a} - T_{k}} \right)} - {\Delta T_{c}}} \right)}}}} \approx {{\overset{\_}{Q}\left( \overset{\_}{T} \right)} + {{\rho c}{\overset{\_}{f}\left( {{x\left( {T_{a} - \overset{\_}{T}} \right)} - {\Delta T_{c}}} \right)}}}}$

according to some embodiments. The aggregated moisture model is:

$\begin{matrix}{{\rho\overset{\_}{V}\frac{d\;\overset{\_}{\omega}}{dt}} = {\overset{\_}{w} + {\rho{\sum\limits_{k}{f_{k}\left( {{x\left( {\omega_{a} - \omega_{k}} \right)} - {\Delta\omega_{c}}} \right)}}}}} \\{\approx {\overset{\_}{w} + {\rho{\overset{\_}{f}\left( {{x\left( {\omega_{a} - \overset{\_}{\omega}} \right)} - {\Delta\omega_{c}}} \right)}}}}\end{matrix}$

according to some embodiments. In some embodiments, the aggregatedthermal and moisture models are aggregate thermal models. Step 608 canbe optional. Step 608 can be performed by model manager 416.

Process 600 includes populating any of the temperature model, thehumidity model, the infectious quanta model, or the aggregated modelsusing sensor data or stored values (step 610), according to someembodiments. In some embodiments, step 610 is performed by model manager416. In some embodiments, step 610 is optional. Step 610 can beperformed based on sensor data obtained from zone sensors 312.

Process 600 includes determining an objective function including a costof operating an HVAC system that serves the zones (step 612), accordingto some embodiments. In some embodiments, step 612 is performed byoptimization manager 412 using the dynamic models and/or the aggregatedmodels provided by model manager 416. The objective function may be asummation of the energy consumption, energy cost, or other variable ofinterest over a given time period. The instantaneous energy consumptionat a discrete time step is given by:

E=η _(coil) ρf (cΔT _(c) +LΔω _(c))+η_(UV)λ_(UV)

which can be summed or integrated over all time steps of the given timeperiod as follows:

${\int_{0}^{T}{{E(t)}dt}} \approx {\Delta{\sum\limits_{t}E_{t}}}$

where Δ is the duration of a discrete time step, according to someembodiments.

Process 600 includes determining one or more constraints for theobjective function including an infection probability constraint (step614), according to some embodiments. In some embodiments, step 614 isperformed by constraint generator 410. The one or more constraints caninclude the infection probability constraint, temperature bounds orconstraints, humidity bounds or constraints, fresh-air ventilationbounds or constraints, VAV flow bounds or constraints, and/oroutdoor-air damper bounds or constraints. The infection probabilityconstraint is:

${{{{M\eta} + {\sum\limits_{t}\mu_{t}}} \leq {{- \frac{1}{p\Delta}}{\log\left( {1 - P^{\max}} \right)}}}{\mu_{t} + \eta}} \geq {N_{t}\ {\forall{t\mspace{14mu}{or}\text{:}}}}$${N_{t} \leq N_{t}^{\max}} = {{- \frac{1}{Mp\Delta}}{\log\left( {1 - P^{\max}} \right)}}$

according to some embodiments.

Process 600 includes performing an optimization to determine controldecisions for HVAC equipment of the HVAC system, and ultraviolet lightsof the HVAC system such that the one or more constraints are met and thecost is minimized (step 616), according to some embodiments. Step 616can be performed by optimization manager 412 by minimizing the objectivefunction subject to the one or more constraints (e.g., the temperature,humidity, etc., bounds and the infection probability constraint). Step616 can also include constructing the optimization problem andconstructing the optimization problem based on the objective function,the dynamic models (or the aggregated dynamic models), and the one ormore constraints. The control decisions can include a fresh-air fractionx for an AHU of the HVAC system (e.g., AHU 304), whether to turn on oroff the UV lights, etc.

Off-Line Optimization Process

Referring particularly to FIG. 7, a process for performing an off-lineoptimization to determine equipment configurations that minimize energyconsumption or cost and satisfy an infection probability constraint isshown, according to some embodiments. Process 700 may share similaritieswith process 600 but can be performed in an off-line mode (e.g., withoutdetermining control decisions or based on real-time sensor data) todetermine or assess various design decisions and provide designinformation to a building manager. Process 700 can be performed bycontroller 310 when configured for the off-line mode (as shown in FIG.5).

Process 700 includes steps 702-708 that can be the same as steps 602-608of process 600. However, while step 608 may be optional in process 600so that the optimization can be performed using a combination ofindividual dynamic models and aggregate dynamic models, step 708 may benon-optional in process 700. In some embodiments, using the aggregatedynamic models reduces a computational complexity of the optimizationfor process 700. Process 700 can be performed for a wide variety ofdesign parameters (e.g., different equipment configurations) whereasprocess 600 can be performed for a single equipment configuration (e.g.,the equipment configuration that process 600 is used to optimize).Therefore, it can be advantageous to use aggregate models in process 700to reduce a complexity of the optimization problem.

Process 700 includes populating the aggregated models using simulationdata (step 710). In some embodiments, step 710 is performed by modelmanager 416 using outputs from simulation database 424 (e.g., usingvalues of various parameters of the aggregate models that are stored insimulation database 424). In some embodiments, step 710 is performedusing known, assumed, or predetermined values to populate the aggregatedmodels.

Process 700 includes determining an objective function including a costof operating an HVAC system that serves the zones (step 712), anddetermining one or more constraints for the objective function includingan infection probability constraint (step 714), according to someembodiments. In some embodiments, step 712 and step 714 are similar toor the same as steps 612 and 614 of process 600.

Process 700 includes performing a sequence of one-step optimizations forvarious equipment configurations to estimate an operating costassociated with that equipment configuration (step 716), according tosome embodiments. In some embodiments, step 716 is performed byoptimization manager 412. Optimization manager 412 can constructdifferent optimization problems for different equipment configurationsusing the aggregate temperature model, the aggregated humidity model,the aggregated infectious quanta model, the one or more constraints, andthe objective function. In some embodiments, optimization manager 412 isconfigured to solve the optimization problems for the differentequipment configurations over a single time step. The results of theoptimizations problems can be output to results manager 418 fordisplaying to a user.

Process 700 includes outputting design suggestions or optimizationsresults to a user (step 718), according to some embodiments. In someembodiments, step 718 includes outputting costs associated withdifferent equipment configurations (e.g., equipment configurations thatinclude UV lights for disinfection and/or filters for disinfection) to auser (e.g., via a display device) so that the user (e.g., a buildingmanager) can determine if they wish to purchase additional disinfectionequipment (e.g., UV lights and/or filters). For example, step 718 caninclude operating a display to provide graph 800 (or a similar graph) toa user.

Although process 700 is described primarily as an “off-line” process, itshould be understood that process 700 is not limited to off-lineimplementations only. In some embodiments, process 700 can be used whencontroller 310 operates in an on-line mode (as described with referenceto FIGS. 4 and 6). In some embodiments, the results generated byperforming process 700 and/or the results generated when operatingcontroller 310 in the off-line mode (e.g., recommended equipmentconfigurations, recommended operating parameters, etc.) can be used toperform on-line control of HVAC equipment or perform other automatedactions. For example, controller 310 can use the recommended equipmentconfigurations to automatically enable, disable, or alter the operationof HVAC equipment in accordance with the recommended equipmentconfigurations (e.g., enabling the set of HVAC equipment associated withthe lowest cost equipment configuration identified by thesimulations/optimizations). Similarly, controller 310 can use therecommended operating parameters to generate and provide control signalsto the HVAC equipment (e.g., operating the HVAC equipment in accordancewith the recommended operating parameters).

In general, the controller 310 can use the optimization/simulationresults generated when operating controller 310 in the off-line mode togenerate design data including one or more recommended design parameters(e.g., whether to include or use UV lights 306 for disinfection, whetherto include or use filter 308 for disinfection, whether to usefresh/outdoor air for disinfection, a recommended type or rating of UVlights 306 or filter 308, etc.) as well as operational data includingone or more recommended operational parameters (e.g., the fraction offresh/outdoor air that should exist in the supply air provided to thebuilding zone, operating decisions for UV lights 306, an amount ofairflow to send to each building zone, etc.). The design data mayinclude a recommended equipment configuration that specifies which HVACequipment to use in the HVAC system to optimize the energy consumption,energy cost, carbon footprint, or other variable of interest whileensuring that a desired level of disinfection is provided.

Controller 310 can perform or initiate one or more automated actionsusing the design data and/or the operational data. In some embodiments,the automated actions include automated control actions such asgenerating and providing control signals to UV lights 306, AHU 304, oneor more VAV units, or other types of airside HVAC equipment that operateto provide airflow to one or more building zones. In some embodiments,the automated action include initiating a process to purchase or installthe recommended set of HVAC equipment defined by the design data (e.g.,providing information about the recommended set of HVAC equipment to auser, automatically scheduling equipment upgrades, etc.). In someembodiments, the automated actions include providing the design dataand/or the operational data to a user interface device (e.g., displaydevice 422) and/or obtaining user input provided via the user interfacedevice. The user input may indicate a desired level of disinfectionand/or a request to automatically update the results of theoptimizations/simulations based on user-selected values that define thedesired infection probability or level of disinfection. Controller 310can be configured to provide any of a variety of user interfaces(examples of which are discussed below) to allow a user to interact withthe results of the optimizations/simulations and adjust the operation ordesign of the HVAC system based on the results.

User Interfaces

Referring now to FIGS. 5 and 9, in some embodiments, user input device420 is configured to provide a user interface 900 to a user. An exampleof a user interface 900 that can be generated and presented via userinput device 420 is shown in FIG. 9. User interface 900 may allow a userto provide one or more user inputs that define which equipment areavailable in the building or should be considered for design purposes(e.g., filtration, UV, etc.) as well as the desired infectionprobability (e.g., low, medium, high, percentages, etc.). The inputsprovided via user interface 900 can be used by controller 310 to set upthe optimization problem or problems to be solved by optimizationmanager 412. For example, constraint generator 410 can use the inputsreceived via user interface 900 to generate the various bounds,boundaries, constraints, infection probability constraint, etc., thatare used by optimization manager 412 to perform the optimization. Aftercompleting all of the simulation scenarios, the results can be presentedto the user via the “Results” portion of user interface 900 that allowsthe user to explore various tradeoffs.

As an example, the “Building Options” portion of user interface 900allows the user to specify desired building and climate parameters suchas the square footage of the building, the city in which the building islocated, etc. The user may also specify whether UV disinfection and/oradvanced filtration should be considered in the simulation scenarios(e.g., by selecting or deselecting the UV and filtration options). The“Disinfection Options” portion of user interface 900 allows the user tospecify the desired level of disinfection or infection probability. Forexample, the user can move the sliders within the Disinfection Optionsportion of user interface 900 to define the desired level ofdisinfection for each month (e.g., low, high, an intermediate level,etc.). Alternatively, user interface 900 may allow the user to definethe desired level of disinfection by inputting infection probabilitypercentages, via a drop-down menu, by selecting or deselectingcheckboxes, or any other user interface element.

After specifying the desired parameters and clicking the “Run” button,optimization manager 412 may perform one or more simulations (e.g., bysolving one or more optimization problems) using the specifiedparameters. Once the simulations have completed, results may bedisplayed in the “Results” portion of user interface 900. The resultsmay indicate the energy cost, energy consumption, carbon footprint, orany other metric which optimization manager 412 seeks to optimize foreach of the design scenarios selected by the user (e.g., UV+Filtration,UV Only, Filtration Only, Neither). The results may also indicate thedaily infection probability for each of the design scenarios (e.g., meaninfection probability, minimum infection probability, maximum infectionprobability). In some embodiments, an initial simulation or simulationsare run using default settings for the disinfection options. In someembodiments, the results include equipment recommendations (e.g., useUV+Filtration, use UV Only, use Filtration Only, use Neither). Theresults of each simulation can be sorted to present the most optimalresults first and the least optimal results last. For example, userinterface 900 is shown presenting the simulation result with the leastenergy consumption first and the most energy consumption last. In otherembodiments, the results can be sorted by other criteria such asinfection probability or any other factor.

The user can adjust desired disinfection options on a monthly basis(e.g., by adjusting the sliders within the Disinfection Options portionof user interface 900), at which point the results may be re-calculatedby averaging over the appropriate subset of simulation instances, whichcan be performed in real time because the simulations need not repeated.Advantageously, this allows the user to adjust the disinfection optionsand easily see the impact on energy cost, energy consumption, carbonfootprint, etc., as well as the impact on infection probability for eachof the design scenarios. Additional display options beyond what is shownin FIG. 9 may be present in various embodiments, for example toselectively disable UV and/or filtration in certain months or toconsider worst-case instances for each month rather than mean values. Inaddition, various other graphical displays could be added to providemore detailed results. User interface 900 may initially presentoptimization results and/or equipment recommendations based on defaultsettings, but then the user is free to refine those settings andimmediately see updates to cost estimates and suggested equipment.

Although a specific embodiment of user interface 900 is shown in FIG. 9,it should be understood that this example is merely one possible userinterface that can be used in combination with the systems and methodsdescribed herein. In general, controller 310 can operate user inputdevice 420 to provide a user interface that includes various sliders,input fields, etc., to receive a variety of user inputs from the uservia user input device 420. In some embodiments, user input device 420 isconfigured to receive a desired level of disinfection, a desired levelof infection probability, etc., from the user and provide the desiredlevel of disinfection, or desired level of infection probability toconstraint generator 410 as the user input(s). In some embodiments, theuser interface includes a knob or a slider that allows the user toadjust between a level of energy savings and a level of infectioncontrol. For example, the user may adjust the knob or slider on the userinput device 420 to adjust the infection probability constraint (e.g.,to adjust thresholds or boundaries associated with the infectionprobability constraint). In some embodiments, the user

In some embodiments, an infection spread probability is treated byconstraint generator 410 as a constraint, or as a value that is used byconstraint generator 410 to determine the infection probabilityconstraint. If a user desires to provide a higher level of disinfection(e.g., a lower level of infection spread probability) and therefore anincreased energy consumption or energy consumption cost, the user mayadjust the knob or slider on the user interface of user input device 420to indicate a desired trade-off between energy consumption and infectionprobability. Likewise, if the user desired to provide a lower level ofdisinfection (e.g., a higher level of infection spread probability) andtherefore a lower energy consumption or energy consumption cost, theuser may adjust the knob or slider on the user interface of the userinput device 420 to indicate such a desired tradeoff between energyconsumption or energy consumption cost and disinfection control.

In some embodiments, user input device 420 is configured to provideanalytics, data, display data, building data, operational data,diagnostics data, energy consumption data, simulation results, estimatedenergy consumption, or estimated energy consumption cost to the user viathe user interface of user input device 420. For example, resultsmanager 418 may operate the user input device 420 and/or the displaydevice 422 to provide an estimated energy consumption or energyconsumption cost to the user (e.g., results of the optimization ofoptimization manager 412 when operating in either the on-line oroff-line mode/configuration). In some embodiments, user input device 420and display device 422 are a same device (e.g., a touchscreen displaydevice, etc.) that are configured to provide the user interface, whilein other embodiments, user input device 420 and display device 422 areseparate devices that are configured to each provide their ownrespective user interfaces.

For example, controller 310 can perform the off-line or planning ordesign tool functionality as described in greater detail above inreal-time (e.g., as the user adjusts the knob or slider) to determine anestimated energy consumption or energy consumption cost given aparticular position of the knob or slider (e.g., given a particulardesired level of infection or disinfection control as indicated by theposition of the knob or slider). In some embodiments, controller 310 isconfigured to operate the user input device 420 and/or the displaydevice 422 to provide or display the estimated energy consumption orestimated energy consumption cost as the user adjusts the knob orslider. In this way, the user can be informed regarding an estimation ofcosts or energy consumption associated with a specific level ofdisinfection control (e.g., with a particular infection probabilityconstraint). Advantageously, providing the estimation of costs or energyconsumption associated with the specific level of disinfection controlto the user in real-time or near real-time facilitates the userselecting a level of disinfection control that provides sufficient ordesired disinfection control in addition to desired energy consumptionor energy consumption costs.

Pareto Optimization

Referring now to FIG. 10, a graph 1000 illustrating a Pareto searchtechnique which can be used by controller 310 is shown, according to anexemplary embodiment. In some cases, users may want a more detailedtradeoff analysis than merely comparing a set of optimization resultsfor a set of selected infection probabilities. For such cases,controller 310 may use a more detailed Pareto search that iterativelydetermines points on a Pareto front 1002 for an energy cost vs.infection probability tradeoff curve. By running additional simulations,this tradeoff curve can be plotted as accurately as possible so thatusers can fully evaluate the entire continuum of infectionprobabilities, (e.g., to look for natural breakpoints where additionaldisinfection probability begins to get more expensive).

To determine the points on the Pareto front 1002, controller 310 maystart with a small number of infection probabilities already simulatedfor a given month and plot them against monthly energy cost. Then,additional candidate infection probabilities can be selected (e.g., asthe points furthest from already completed simulations). Aftersimulating instances with the new infection probabilities, these pointsare added to the plot, and the process repeats to the desired accuracy.Many criteria for selecting new points are possible, but one possiblestrategy is to choose the midpoint of successive points with the largestarea (i.e., of the rectangle whose opposite corners are given by the twoexisting points) between them. This strategy prioritizes regions wherethe curve is changing rapidly and leads to efficient convergence.

As an example, consider the case in graph 1000. The goal is to obtain anapproximation of the true Pareto front 1002, which is illustrated inFIG. 10 for ease of explanation, but may not be truly known. Theinstances of the optimization run for the small number of infectionprobabilities result in the points marked with squares in graph 1000 forIteration 0. This gives a very coarse approximation of the true front.Controller 310 may then select new points in each iteration, run thosesimulations, and add those points to graph 1000. For example, the pointsmarked with diamond shapes in graph 1000 show the points selected forIteration 1 the points marked with triangles in graph 1000 show thepoints selected for Iteration 2, the points marked with invertedtriangles in graph 1000 show the points selected for Iteration 3, andthe points marked with circles in graph 1000 show the points selectedfor Iteration 4. By the end of Iteration 4, the empirical Pareto frontis a good approximation of the true front 1002, and of course additionaliterations can be performed to further improve accuracy. The empiricalPareto front generated using this technique can be used by controller300 to solve a Pareto optimization problem to determine an optimaltradeoff between the costs and benefits of selecting different infectionprobability values in the infection probability constraint.

In some embodiments, determining the infection probability constraint(e.g., to provide an optimal level of disinfection control, or anoptimal level of infection probability spread) and the resulting energyconsumption or energy consumption costs required for HVAC system 200 tooperate to achieve the infection probability constraint is a Paretooptimization problem. For example, at a certain point, additionaldisinfection control may require undesirably high energy consumption orenergy consumption costs. In some embodiments, controller 310 may solvea Pareto optimization problem given various inputs for the system todetermine one or more inflection points along a curve between cost(e.g., energy consumption or energy consumption cost) and a benefit(e.g., disinfection control, infection probability, disinfection, etc.)or to determine an optimal tradeoff between the cost and the benefit.

In some embodiments, controller 310 is configured to operate displaydevice 422 and/or user input device 420 to provide an infectionprobability constraint associated with the optimal tradeoff between thecost and the benefit. In some embodiments, controller 310 can operateaccording to various modes that can be selected by the user via the userinterface of user input device 420. For example, the user may opt for afirst mode where controller 310 solves the Pareto optimization problemto determine the infection probability constraint associated with theoptimal tradeoff point between the cost (e.g., the energy consumption orenergy consumption cost) and the benefit (e.g., the disinfectioncontrol, a provided level of disinfection, an infection probability,etc.). In the first mode, the controller 310 can automatically determinethe infection probability constraint based on the results of the Paretooptimization problem. In some embodiments, controller 310 still operatesdisplay device 422 to provide estimated, actual, or current energyconsumption or energy consumption costs and infection probabilityconstraints.

In a second mode, controller 310 can provide the user the ability tomanually adjust the tradeoff between the cost and the benefit (e.g., byadjusting the slider or knob as described in greater detail above). Insome embodiments, the user may select the desired tradeoff betweeninfection control and energy consumption or energy consumption costsbased on the provided estimations of energy consumption or energyconsumption costs.

In a third mode, controller 310 can provide the user additional manualabilities to adjust the infection probability constraint directly. Inthis way, the user may specifically select various boundaries (e.g.,linear boundaries if the infection probability constraint is implementedas a linear constraint as described in greater detail above) for theinfection probability constraint. In some embodiments, the user mayselect between the various modes (e.g., the first mode, the second mode,and/or the third mode).

It should be understood that while the Pareto optimization as describedherein is described with reference to only two variables (e.g., energyconsumption or energy consumption cost and disinfection control), thePareto optimization may also account for various comfort parameters orvariables (e.g., temperature and/or humidity of zones 206, eitherindividually or aggregated). In some embodiments, controller 310 mayalso operate display device 422 to provide various comfort parametersthat result from a particular position of the knob or slider that isprovided on the user interface of user input device 420. In someembodiments, additional knobs, sliders, input fields, etc., are alsoprovided on the user interface of user input device 420 to receivevarious inputs or adjustments for desired comfort parameters (e.g.,temperature and/or humidity). In some embodiments, controller 310 (e.g.,results manager 418) is configured to use the dynamic models fortemperature or humidity as described above to determine estimations ofthe various comfort parameters as the user adjusts the knobs or sliders(e.g., the knobs or sliders associated with disinfection control and/orenergy consumption or energy cost consumption). Similarly, controller310 can solve the Pareto optimization problem as a multi-variableoptimization problem to determine an inflection point or a Paretoefficiency on a surface (e.g., a 3d graph or a multi-variableoptimization) which provides an optimal tradeoff between cost (e.g., theenergy consumption, the energy consumption cost, etc.), comfort (e.g.,temperature and/or humidity), and disinfection control (e.g., theinfection probability constraint).

Pareto Optimization Controller

Referring particularly to FIG. 11, a controller 1110 is shown, accordingto some embodiments. The controller 1110 can be similar to thecontroller 310 and can be implemented in the HVAC system 300 asdescribed in greater detail above. In some embodiments, the controller1110 includes the constraint generator 410, the model manager 416, thesimulation database 414, the optimization manager 412, and the resultsmanager 418, similar to the controller 310. The controller 1110additionally includes a Pareto optimizer 1112 that is configured to useoptimization results from the optimization manager 412 and perform aPareto optimization to determine feasible and infeasible operatingpoints, and to determine, from the feasible operating point, which isthe Pareto optimal point. In some embodiments, the optimization resultsprovided to the Pareto optimizer 1112 are or include values of theobjective function. For example, the values of the objective functioncan include values of two or more variables of interest. In someembodiments, the values of the objective function can include energycost and infection risk for an associated pair of decision variablessuch as minimum ventilation setpoint and supply temperature setpoint. Insome embodiments, both the values of the decision variables and valuesof the objective function are provided to the Pareto optimizer 1112 foruse in determining what values of the decision variables should be usedto achieve the Pareto optimal values of the values of the objectivefunction.

In some embodiments, the controller 1110 is operable between anoperational mode and a monitoring mode. For example, when the controller1110 is in the operational mode, the controller 1110 may include thecontrol signal generator 408 instead of the results manager 418 and mayautomatically determine control decisions and operate the AHU 304, theUV lights 306, etc., of the HVAC system 300 based on the determinedcontrol decisions. When the controller 1110 is in the monitoring mode,the controller 1110 may include the results manager 418 (as shown inFIG. 11) and can be configured to provide the display data to thedisplay device 422. In some embodiments, the display device 422 mayoperate to display different control options for the HVAC system 300,and the user may select from the different control options. Theselection can be provided to the controller 1110 or the control signalgenerator 408 and implemented by the controller 1110 to operate the HVACsystem 300 according to the selected control option (e.g., over a futuretime horizon). In some embodiments, the controller 1110 is also operable

In some embodiments, the controller 1110 is configured to use acombination of domain knowledge and artificial intelligence for eitherthe operational mode or the advisory mode. For example, the controller1110 can use domain knowledge including physics-based models for HVACheat and mass transfer, phenomenological models that match systembehavior for regulatory control, and/or different default values of thevarious parameters described herein. In some embodiments, the controller1110 uses the artificial intelligence to train key model parameters(e.g., of the physics-based models described herein) in an online mode(e.g., when the controller 1110 communicates with a remote device,processing circuitry, network, gateway, etc.) using one or moreregression techniques. In some embodiments, the controller 1110 uses theartificial intelligence to predict future disturbances using recent dataobtained from the HVAC system 300 and also using timeseries models.

Referring particularly to FIG. 12, a diagram 1200 illustrating thefunctionality of the controller 1110 is shown, according to someembodiments. The diagram 1200 includes a data model 1202, a modelgenerator 1210, a timeseries resampler 1212, a model tuner 1214, aninput generator 1216, modeling data 1218, a dynamic model simulator1232, analysis mode outputs 1234, a Pareto optimizer 1236, and advisorymode outputs 1240, according to some embodiments. In some embodiments,the data model 1202 includes one or more zone configurations 1204 (e.g.,of zones 206), operational data 1206 (e.g., of the HVAC system 300, orhistorical operational data thereof), and weather forecast data 1208. Insome embodiments, the data model 1202 is stored in the memory 406 of thecontroller 1110. In some embodiments, the data model 1202 is populatedusing data received from various sensors or control decisions of theHVAC system 300 over a previous time period (e.g., the operational data1206). In some embodiments, the data model 1202 is populated usingsystem configuration information such as the zone configurations 1204(e.g., proximity of the zones 206, which of the zones 206 are served bywhich AHUs, etc.). In some embodiments, the data model 1202 is populatedusing information obtained from a third party service such as a weatherservice.

In some embodiments, the modeling data 1218 includes psychometric data1220 of the HVAC system 300, HVAC equipment data 1222, infectionparameters 1224, and/or disturbance schedules 1226. In some embodiments,the HVAC equipment data 1222 includes different performance curves,model identifiers, model numbers, models of HVAC equipment that predictone or more operational parameters (e.g., air delivery, temperature ofair delivered to a zone, etc.) as a function of one or more inputvariables, etc. In some embodiments, the infection parameters 1224 arevalues of any of the variables of the Wells-Riley equations orderivations thereof, quantum concentration models, infection probabilitymodels, CO2 concentration models, infection probability constraints,etc., as described in greater detail above with reference to FIGS. 3 and4. For example, the infection parameters 1224 can include any ofexpected, actual, or hypothetical number of infected individuals D,total number of susceptivle individuals S, number of infectiousindividuals I, disease quanta generation rate q, total exposure time t,quantum concentration in the air N, net indoor CO2 concentration C,total air volume of one or more zones V, net concentration of exhaledCO2 c, number of infectious particles that an individual inhales over agiven time k_([0, T]), the upper boundary on acceptable or desirableinfection probability P_([0, T]) ^(max), infectious quanta removalfraction of a filter λ_(filter), infectious quanta removal of UV lightsλ_(UV), etc. In some embodiments, the disturbance schedules 1226 includeexpected heat disturbances, CO2 disturbances, expected occupancyschedules, etc., or any other schedules of disturbances for variousinfections parameters, environmental parameters, HVAC parameters, etc.In some embodiments, the data model 1202 and/or the modeling data 1218are the domain knowledge that is used for performing the optimizationdescribed herein. In some embodiments, the data model 1202 and themodeling data 1218 are stored in the simulation database 414.

In some embodiments, the modeling data 1218 and the zone configurationdata 1204 is provided to the model generator 1210 for generation of amodel (e.g., any of the models or constraints described in greaterdetail above with reference to FIGS. 3-4). In some embodiments, themodel generator 1210 is configured to perform any of the functionalityof the model manager 416. In some embodiments, the weather forecast data1208 is provided to the timeseries resampler 1212 that is configured toresample the weather forecast data 1208 and output resampled data to themodel tuner 1214 and the input generator 1216. The resampled data has afrequency or time interval that is different than the frequency or timeinterval of the weather forecast data 1208 provided to the timeseriesresampler 1212, according to some embodiments. In some embodiments, thetimeseries resampler 1212 operates to provide the resampled data to themodel tuner 1214 and the input generator 1216 at an appropriatefrequency or time interval (e.g., between data points of the weatherforecast data) so that the model tuner 1214 and the input generator 1216can use the weather forecast data 1208, provided as the resampled data.In some embodiments, the timeseries resampler 1212 is configured toperform interpolation and/or extrapolation techniques to generate theresampled data based on the weather forecast data 1208.

The model tuner 1214 is configured to use the resampled data (e.g., theresampled weather forecast data 1208) to determine data-derivedparameters and provide the data-derived parameters to the modelgenerator 1210, according to some embodiments. In some embodiments, themodel tuner 1214 is configured to generate a disturbance model using theresampled data to predict disturbances that may be introduced to HVACsystem (e.g., temperature fluctuations, humidity fluctuations, etc., dueto weather) and provide parameters of the disturbance model or outputsof the disturbance model to the model generator 1210 as the data-derivedparameters. In some embodiments, the model tuner 1214 is configured tooutput the disturbance model to the input generator 1216. In someembodiments, the data-derived parameters are adjustments, calibrationfactors, additional correction terms, etc., for the model generator 1210so that the model generator 1210 outputs models that accurately predicttemperature, humidity, energy consumption, infection probability, etc.,while accounting for different weather conditions, disturbances,occupancy, etc. In some embodiments, the data-derived parameters aregenerated by the model tuner 1214 using a neural network, a machinelearning technique, artificial intelligence, etc. For example, the modeltuner 1214 can obtain the operational data 1206 or the weather forecast1208 for a historical or previous time period, as well as predictions ofthe various models for the historical or previous time period (e.g.,predictions of zone temperatures, infection risks, infectionprobability, humidity, etc.), and actual values of the predictions ofthe various models for the historical or previous time period (e.g.,actual zone temperatures, actual infection risks, actual infectionprobability, etc., or any other environmental or infection relatedparameter that can be sensed or determined based on sensor data), anddetermine adjustments for the models using the neural network, themachine learning technique, the artificial intelligence, etc., toimprove accuracy of the models.

The model generator 1210 uses the data-derived parameters (e.g.,disturbance parameters, adjustment parameters, correction factors,calibration factors, additional model terms, etc.), the zoneconfigurations 1204, and the modeling data 1218 to generate one or moremodels and output model parameters (shown in FIG. 12 as “genericparameters”) to the dynamic model simulator 1232, according to someembodiments. In some embodiments, the model generator 1210 uses theparameters of the disturbance model to tune or adjust the modelgenerated based on the zone configuration data 1204 and the modelingdata 1218. In some embodiments, the models (e.g., the genericparameters) are the dynamic models (e.g., the dynamic temperature model,the dynamic humidity model, the dynamic infectious quanta model, etc.)as described in greater detail above with reference to FIGS. 3-5.

The input generator 1216 uses the resampled data provided by thetimeseries resampler 1212 and the disturbance model provided by themodel tuner 1214 to determine model timeseries inputs, according to someembodiments. In some embodiments, the input generator 1216 is configuredto generate timeseries inputs for various extrinsic parameters such asambient or outdoor temperature, ambient or outdoor humidity, price perunit of energy as provided by a utility provider, etc. The inputgenerator 1216 may provide the model timeseries inputs to the dynamicmodel simulator 1232 for use in performing a simulation (e.g., either tospecific model forms 1228 or to generic model simulation 1230),according to some embodiments. In some embodiments, the model timeseriesinputs are predicted or estimated timeseries data for a future timeperiod, or are historical data from a previous time period (e.g., forthe advisory mode outputs 1240 and the analysis mode outputs 1234,respectively). The input generator 1216 can provide specific modelparameters to the specific model forms 1228 of the dynamic modelsimulator 1232 so that different generic models can be simulated for aspecific HVAC system, a specific building, a specific space or zone,etc. The specific model parameters can be various thermalcharacteristics (e.g., heat transfer or heat storage parameters), HVACequipment model numbers, HVAC equipment operating curves, etc.

The dynamic model simulator 1232 is configured to use the specific modelparameters and the model timeseries inputs to perform a simulation for afuture time period, and to perform a simulation or analysis for aprevious time period, according to some embodiments. In someembodiments, the dynamic model simulator 1232 includes specific modelforms 1228 and generic model simulation 1230. In some embodiments, thespecific model forms 1228 are determined based on predefined or genericmodels (e.g., generic versions of the dynamic models as described ingreater detail above) with specific model parameters that are generatedor adjusted based on outputs of the model tuner 1214 and real-world oractual data as provided by the data model 1202 (e.g., the zoneconfiguration data 1204, the operational data 1206, the weather forecastdata 1208, etc.).

In some embodiments, the generic model simulation 1230 is performedusing the specific model forms 1228 for both a future time period (e.g.,for the advisory mode outputs 1240) and for a previous time period(e.g., for the analysis mode outputs 1234). In some embodiments, thegeneric model simulation 1230 is performed to determine energyconsumption or energy cost and associated infection risks ordisinfection (e.g., a reduction in infection risks resulting fromperforming any of the fresh air intake operations of an AHU, UV lightdisinfection, or filtration). In some embodiments, the generic modelsimulation 1230 uses the dynamic infectious quanta model to simulate orassess infection risks for previously performed HVAC operations, or forpredicted future HVAC operations.

The outputs of the generic model simulation 1230 (e.g., objectivefunction values such as including but not limited to infection risk andenergy cost) are provided to the Pareto optimizer 1236 and the analysismode outputs 1234, according to some embodiments. In some embodiments,the outputs of the dynamic model simulator 1232 that use historical BMSdata (e.g., infection risk and energy cost values associated withprevious operation of the HVAC system over the previous time period) areprovided as the analysis mode outputs 1234. In some embodiments, theoutput of the dynamic model simulator 1232 that are for the future timeperiod (e.g., for different possible control decisions of the HVACsystem or decision variables over the future time period) are providedto the Pareto optimizer 1236 for determination of the advisory modeoutputs 1240 (e.g., using the Pareto optimization techniques describedin greater detail below with reference to FIGS. 13-16).

Pareto Optimization Techniques

Referring particularly to FIGS. 13-16, the Pareto optimizer 1236 or thePareto optimizer 1112 are configured to perform various Paretooptimization techniques as described herein to determine Paretooptimization results, according to some embodiments. It should beunderstood that while the techniques described herein with reference toFIGS. 13-16 are described as being performed by the Pareto optimizer1236, the techniques can also be performed by the Pareto optimizer 1112or processing circuitry 402 thereof.

Referring particularly to FIG. 13, a diagram 1300 shows a graph 1302 ofdifferent decision variables, and a graph 1304 of correspondingobjective function values for each of the different decision variables.The graph 1302 shows different combinations for a supply temperaturesetpoint and a minimum ventilation setpoint (shown on the Y and X axes,respectively) for the HVAC system 300, according to some embodiments. Itshould be understood that only two decision variables are shown for easeof explanation, and that any number of decision variables may be used.Different values and combinations of both the decision variables arerepresented in FIG. 13 as points 1306. For example, points 1306 a-1306 dhave a same value for the minimum ventilation setpoint decisionvariables but different values of the supply temperature setpointdecision variable. Similarly, points 1306 e-1306 h have the same valuefor the minimum ventilation setpoint decision (different than the valueof the minimum ventilation setpoint decision variable for points 1306a-1306 d) but different values of the supply temperature setpointdecision variable. Points 1306 i-1306 l likewise have the same value ofthe minimum ventilation setpoint decision variable (different than thevalues of the minimum ventilation setpoint decision variable for points1306 a-1306 d and 1306 e-1306 h) but different values of the supplytemperature setpoint decision variable. In some embodiments, the valuesof the decision variables are a fixed set (e.g., generated as a gridusing minimum and maximum allowed values for each of the multipledecision variables) or are generated iteratively based on simulationresults (e.g., by adding additional points that are likely to be Paretooptimal based on simulation results of proximate points).

In some embodiments, a simulation is performed to determinecorresponding energy cost and infection risk for each of the differentpoints 1306. The corresponding energy cost and infection risk are shownas points 1308 in graph 1304. In some embodiments, points 1308 a-1308 lof graph 1304 correspond to points 1306 a-1306 l of graph 1302. Forexample, point 1308 a illustrates the corresponding energy cost andinfection risk for the values of the minimum ventilation setpoint andthe supply temperature of the point 1306a. Likewise, points 1308 b-1308l illustrate the various corresponding energy costs and infection risksfor each of the minimum ventilation setpoint and supply temperaturesetpoint values as represented by points 1306 b-1306 l. In someembodiments, each of the points 1306 a-1306 l and the correspondingpoints 1308 a-1308 l correspond to a simulation performed by theoptimization manager 412, or the dynamic model simulator 1232. Forexample, the dynamic model simulator 1232 may perform a simulation foreach of the sets of values of the supply temperature setpoint and theminimum ventilation setpoint (e.g., the decision variables) and outputvalues of the energy cost and infection risk for each simulation (shownas points 1308). It should be understood that while FIG. 13 shows onlytwo objectives of the Pareto optimization (e.g., energy cost andinfection risk), the Pareto optimization may have any number ofoptimization objectives (e.g., more than two, etc.).

Referring particularly to FIG. 14, a diagram 1400 shows the graph 1304and a graph 1310, according to some embodiments. The graph 1304 showsthe points 1308 that illustrate the various combinations of energy costand infection risk for the corresponding values of the decisionvariables (the supply temperature setpoint and the minimum ventilationsetpoint shown in graph 1302 in FIG. 13). In some embodiments, the graph1310 illustrates groups 1312 that are include the points 1308 groupedaccording to feasibility, and further group according to Paretooptimality. Specifically, groups 1312 includes a first group of points1312 a (e.g., points 1308 i and 1308 e), a second group of points 1312 b(e.g., points 1308 f, 1308 a, 1308 b, 1308 c, and 1308 d), and a thirdgroup of points 1312 c (e.g., points 1308 j, 1308 k, 1308 l, 1308 g, and1308 h).

The first group of points 1312 a are points that are infeasible,unfeasible, or non-feasible. In some embodiments, the Pareto optimizer1236 is configured to determine or identify which of the points 1308 areinfeasible and group such combinations of energy cost and infection riskas infeasible solutions. In some embodiments, the Pareto optimizer 1236is configured to use threshold energy costs or infection risks, and ifsome of the points 1308 are greater than a maximum allowable energy costor infection risk, or less than a minimum allowable infection risk orenergy cost, the Pareto optimizer 1236 can determine that such pointsare infeasible and group them accordingly as the first group of points1312 a. In some embodiments, the maximum or minimum allowable energycost or infection risk values used by the Pareto optimizer 1236 are userinputs, values set by legal regulations, or values determined based onabilities of the HVAC system 300. In some embodiments, the second groupof points 1312 b and the third group of points 1312 c are feasiblesolutions.

In some embodiments, the Pareto optimizer 1236 is configured to performa Pareto optimization based on the points 1308 to determine which of thepoints 1308 are Pareto optimal. A Pareto optimal point is a point whereneither the energy cost or the infection risk can be reduced withoutcausing a corresponding increase in the infection risk or the energycost. In the example shown in FIG. 14, the points 1308 j, 1308 k, 1308l, 1308 g, and 1308 h are Pareto optimal points, and the Paretooptimizer 1236 is configured to classify these points as such, therebydefining the third group of points 1312 c, according to someembodiments. In some embodiments, the Pareto optimizer 1236 isconfigured to determine that points which are feasible but are notPareto optimal (e.g., points 1308 f, 1308 a, 1308 b, 1308 c, and 1308 d)should define the second group of points 1312 b. In this way, the Paretooptimizer 1236 can define several groups of the points 1308 (e.g.,groups of various solutions to be considered): (i) infeasible points,(ii) feasible points that are Pareto optimal, and (iii) feasible pointsthat are not Pareto optimal.

Referring particularly to FIG. 15, the Pareto optimizer 1236 can furtheridentify which of the Pareto optimal points, shown as the third group ofpoints 1312 c in graph 1310, result in maximum disinfection (e.g.,minimal infection risk), minimum energy consumption, and an equalpriority between disinfection and energy consumption, according to someembodiments. In some embodiments, the Pareto optimizer 1236 isconfigured to determine which of the Pareto optimal points (i.e., thepoints 1308 of the third group of points 1312 c) have a minimuminfection risk, a minimum energy consumption, and an equal prioritybetween energy consumption and infection risk. Specifically, in theexample shown in FIGS. 13-15, the point 1308 j is a Pareto optimal pointthat has a lowest infection risk, and therefore the Pareto optimizer1236 identifies point 1308 j as a maximum disinfection point 1318.Similarly, in the example shown in FIGS. 13-15, the Pareto optimizer1236 determines that the point 1308 h is a Pareto optimal pointassociated with minimum energy consumption, and therefore the Paretooptimizer 1236 identifies the point 1308 h as a minimum energyconsumption point 1322. Finally, in the example shown in FIGS. 13-15,the Pareto optimizer 1236 determines that the point 1308 l is a Paretooptimal point that results in an equal priority between the infectionrisk and the energy consumption, shown as equal priority point 1320.

In some embodiments, the maximum disinfection point 1318 (e.g., point1308 j), the minimum energy consumption (or energy costs) point 1322(e.g., point 1308 h), and the equal priority point 1320 (e.g., point1308 l) are the Pareto optimization results. In some embodiments, thePareto optimization results also include the energy cost, infectionrisk, as well as the minimum ventilation setpoint, and the supplytemperature setpoint for each of the maximum disinfection point 1318,the minimum energy consumption point 1322, and the equal priority point1320. In some embodiments, the Pareto optimization results are providedto the user via the display device 422 for selection. For example, thedisplay device 422 can provide different recommended operatingpossibilities such as a maximum disinfection operating possibility, aminimum energy consumption operating possibility, and an equal energyand infection risk. In some embodiments, the user may select one of thedifferent operating recommendations, and provide the selection to thecontroller 1110 for use in operating the HVAC system 300 according tothe selected operating possibility.

Referring particularly to FIG. 16, a diagram 1600 shows another exampleof a graph 1602 and a graph 1604 illustrating the functionality of thePareto optimizer 1236, according to some embodiments. Graph 1602includes points 1622 that illustrate different combinations of minimumventilation and supply temperature setpoint (e.g., the decisionvariables) usable by the dynamic model simulator 1232 or theoptimization manager 412 for performing a simulation to determinecorresponding infection risk and energy costs (shown as points 1612 ingraph 1604), according to some embodiments. In some embodiments, thepoints 1612 illustrated in the graph 1604 are mapped to the points 1622.For example, the simulation can be performed for each of the points 1622to determine the corresponding infection risk and energy cost, asrepresented by points 1612 in graph 1604.

In the example shown in FIG. 16, the Pareto optimizer 1236 identifies agroup 1620 of infeasible points, according to some embodiments. Theinfeasible points may be points that cannot be achieved due toconstraints and operational ability of the HVAC system 300. In someembodiments, the Pareto optimizer 1236 further identifies which of thepoints 1612 are Pareto optimal points, and determines which of thePareto optimal points are associated with lowest infection risk (e.g.,maximum disinfection), lowest energy costs or energy consumption, and abalanced priority point where energy costs and infection risk areequally prioritized. In the example shown in FIG. 16, the Paretooptimizer 1236 identifies that a point 1618 of graph 1604 is the Paretooptimal point that results in lowest infection risk, which correspondsto point 1610 of graph 1602. Similarly, the Pareto optimizer 1236 maydetermine that the point 1614 is the Pareto optimal point that resultsin lowest energy cost, which corresponds to the point 1606 in graph1602, according to some embodiments. Finally, the Pareto optimizer 1236can determine that a point 1616 of graph 1604 is a Pareto optimal pointthat results in a solution with equal priority between the infectionrisk and the energy cost, which corresponds to point 1608 of graph 1602,according to some embodiments.

In some embodiments, the Pareto optimizer 1236 is configured to provideall of the Pareto optimal points to the user via the display device 422.In some embodiments, the Pareto optimizer 1236 or the Pareto optimizer1112 is configured to provide the Pareto optimal points as the Paretooptimal results to the results manager 418 for use in display to theuser. In some embodiments, the Pareto optimizer 1112 or the Paretooptimizer 1236 automatically selects one of the Pareto optimal pointsfor use and provides the Pareto optimal points and its associatedcontrol decisions (e.g., the minimum ventilation and supply temperaturesetpoints) to the control signal generator 408.

Pareto Optimization Process

Referring particularly to FIG. 17, a process 1700 for performing aPareto optimization to determine operation of a building HVAC system isshown, according to some embodiments. Process 1700 includes steps1702-1716 and can be performed by the controller 1110 or morespecifically, by the Pareto optimizer 1112, according to someembodiments. In some embodiments, process 1700 is performed to determinevarious Pareto optimal values, or to determine a Pareto optimal solutionand associated operating parameters that results in optimal tradeoffbetween infection risk and energy cost.

Process 1700 includes obtaining multiple sets of values of controldecision variables, each set of values including a different combinationof the control decision variables (step 1702), according to someembodiments. In some embodiments, the control decision variables includea minimum ventilation setpoint and a supply temperature setpoint. Insome embodiments, the control decision variables include operatingparameters or control decisions of the UV lights 306 or the AHU 304(e.g., a fresh air intake fraction x). It should be understood that thecontrol decision variables described herein are not limited to only twovariables, and may include any number of variables. In some embodiments,each set of the values of the control decision variables is a uniquecombination of different values of the control decision variables. Forexample, graph 1302 of FIG. 13 shows different unique combinations ofvalues of supply temperature setpoint and minimum ventilation setpoint.Similarly, regardless of a number of control decision variables, eachset of the values of the control decision variables may be a uniquecombination, according to some embodiments.

Process 1700 includes performing a simulation for each set of the valuesof the control decision variables to determine sets of values of energycost and infection risk (step 1704), according to some embodiments. Insome embodiments, the simulation is performed using the dynamic modelsas generated by the model manager 416, or using the techniques of thedynamic model simulator 1232 (e.g., the specific model forms 1228, thegeneric model simulation 1230, etc.). In some embodiments, thesimulations are performed by the controller 1110, or processingcircuitry 402 thereof. In some embodiments, the simulations areperformed for a future time horizon to generate predicted or simulatedvalues for the energy cost and infection risk. In some embodiments, thesimulations are performed for a previous or historical time period todetermined values of the energy cost and infection risk for analysis(e.g., for comparison with actual historical data of the energy cost andinfection risk). In some embodiments, each of the sets of values ofcontrol decisions (e.g., as obtained in step 1702) is used for aseparate simulation to determine a corresponding set of performancevariables (e.g., the values of energy cost and infection risk). In someembodiments, the simulations are performed subject to one or moreconstraints. In some embodiments, step 1704 includes performing steps602-616 of process 600. In some embodiments, step 1704 includesperforming steps 702-716 of process 700.

Process 1700 includes determining which of the sets of values of energycost and infection risk are infeasible and which are feasible (step1706), according to some embodiments. In some embodiments, step 1706 isperformed by the Pareto optimizer 1112 or by the Pareto optimizer 1236.In some embodiments, step 1706 is performed using one or moreconstraints. The one or more constraints can be minimum or maximumallowable values of either of the energy cost and infection risk,according to some embodiments. For example, if one of the sets of valuesof energy cost and infection risk has an energy cost or energyconsumption that exceeds a maximum allowable value of energy cost (e.g.,exceeds a maximum threshold), then such a set of values of energy costand infection risk, and consequently the corresponding sets of values ofthe control decision variables, may be considered infeasible, accordingto some embodiments. In some embodiments, the constraints are set basedon capabilities of an HVAC system that the process 1700 is performed tooptimize, user inputs, budgetary constraints, minimum infection riskreduction constraints, etc.

Process 1700 includes determining which of the feasible sets of valuesof energy cost and infection risk are Pareto optimal solutions (step1708), according to some embodiments. In some embodiments, the step 1708is performed by the Pareto optimizer 1112 or by the Pareto optimizer1236. In some embodiments, the step 1708 is performed to determine whichof the sets of values of energy cost and infection risk are Paretooptimal from the feasible sets of values of energy cost and infectionrisk. In some embodiments, process 1700 includes performing steps1702-1708 iteratively to determine sets of decision variables. Forexample, the decision variables can be iteratively generated based onsimulation results (e.g., by generating additional points that arelikely to be Pareto optimal based on the results of step 1708).

Process 1700 includes determining, based on the Pareto optimalsolutions, a minimum energy cost solution, a maximum disinfectionsolution, and an equal priority energy cost/disinfection solution,according to some embodiments. In some embodiments, step 1710 isperformed the Pareto optimizer 1112 or by the Pareto optimizer 1236. Insome embodiments, the minimum energy cost solution is the set of valuesof the energy cost and infection risk that are Pareto optimal, feasible,and also have a lowest value of the energy cost. In some embodiments,the maximum disinfection solution is selected from the set of values ofthe energy cost and infection risk that are feasible and Pareto optimal,and that has a lowest value of the infection risk. In some embodiments,the equal priority energy cost/disinfection solution is selected fromthe set of values of the energy cost and infection risk that arefeasible and Pareto optimal, and that equally prioritizes energy costand infection risk. For example, the energy cost/disinfection solutioncan be a point that is proximate an inflection of a curve that is fit tothe sets of values of energy cost and infection risk (e.g., includingthe feasible and infeasible points, only the feasible points, only thePareto optimal points, etc.).

Process 1700 includes providing one or more of the Pareto optimalsolutions to a user via a display screen (step 1712), according to someembodiments. In some embodiments, step 1712 includes operating thedisplay device 422 to display the Pareto optimal solutions to the useras different operational modes or available operating profiles. In someembodiments, step 1712 is performed by the display device 422 and thecontroller 1110. In some embodiments, step 1712 includes providing thePareto optimal solutions and historical data (e.g., historical data ofactually used control decisions and the resulting energy cost andinfection risks). In some embodiments, step 1712 is optional. Forexample, if the user has already set a mode of operation (e.g., alwaysuse minimum infection risk settings, always use minimum energy costsolution, always use equal priority energy cost/disinfection solution,etc.), then step 1712 can be optional.

Process 1700 includes automatically selecting one of the Pareto optimalsolutions or receiving a user input of a selected Pareto optimalsolution (step 1714), according to some embodiments. In someembodiments, a user may select a setting for the controller 1110 toeither automatically select one of the Pareto optimal solutions, or thatthe Pareto optimal solutions should be provided to the user forselection. In some embodiments, step 1714 is performed by the controller1110 and the display device 422. For example, step 1714 can be performedby a user providing a selection of one of the Pareto optimal solutions(and therefore the corresponding control decisions) to be used by theHVAC system for operation, according to some embodiments. In someembodiments, step 1714 is performed automatically (e.g., if a user oradministrator has selected a preferred mode of operation for the HVACsystem) by the Pareto optimizer 1112 to select one of the Pareto optimalsolutions and therefore the corresponding control decisions foroperational use of the HVAC system.

Process 1700 includes operating equipment of an HVAC system according tothe control decisions of the selected Pareto optimal solution (step1716), according to some embodiments. In some embodiments, step 1716includes operating the HVAC system 300. More specifically, step 1716 caninclude operating the UV lights 307, the AHU 304, etc., of the HVACsystem 300 according to the control decisions of the selected Paretooptimal solution. Advantageously, using the control decisions of theselected Pareto optimal solution can facilitate optimal control of theHVAC system 300 in terms of risk reduction, energy consumption, or anequal priority between infection risk reduction and energy consumptionor energy cost.

Pareto Optimal Analysis and Advisory

Referring again to FIGS. 11-16, the controller 1110 can be configured toperform any of the Pareto optimization techniques described herein toperform a historical analysis for the building 10 that the HVAC system300 serves. For example, the controller 1110 can use modeling data 1218and/or a data model 1202 that is based on historical data of thebuilding 10, weather conditions, occupancy data, etc. In someembodiments, the controller 1110 is configured to perform the simulationand Pareto optimization techniques to determine different sets of valuesfor the energy cost and infection risk, determine which of these setsare feasible, infeasible, Pareto optimal, etc., and compare thedifferent Pareto optimal solutions to actual energy consumption (e.g.,as read on a meter or other energy consumption sensor) and to estimatedinfection risks that are determined based on historical data of thebuilding 10 or the HVAC system 300. In some embodiments, the analysismode outputs 1234 are configured to determine potential advantages(e.g., missed energy cost or consumption opportunities) that could havebeen achieved if the HVAC system 300 had been operated according to aPareto optimal solution over a previous time period. In someembodiments, the controller 1110 is configured to use newly obtainedenergy cost or energy consumption data and associated infection riskdata (e.g., values of the objective functions) and compare them toenergy cost or energy consumption data and associated infection riskdata of a previous time period (e.g., a same month from a year ago) toprovide the user with information regarding improved efficiency of theHVAC system 300 resulting from operating the HVAC system 300 accordingto a Pareto optimal solution.

Parallel Analysis and Advisory Outputs

Referring again to FIG. 12, the controller 1110 is configured to outputboth analysis mode outputs 1234 and advisory mode outputs 1240concurrently or simultaneously, according to some embodiments. In someembodiments, the controller 1110 is configured to output both theanalysis mode outputs 1234 and the advisory mode outputs 1240 to abuilding administrator or a user as display data via the display device422.

The analysis mode outputs 1234 can be analysis data based on historicaland/or current BMS data, according to some embodiments. In someembodiments, the analysis mode outputs 1234 include energy consumption,infection risks, ventilation setpoints, etc., over a previous timeperiod. In some embodiments, the analysis mode outputs 1234 includessensor or meter data (e.g., of the energy consumption, energy cost,etc.), and one or more calculated values (e.g., the calculated infectionrisk as described using the techniques herein) for the HVAC system 300or the building 10.

In some embodiments, the advisory mode outputs 1240 are the results ofthe Pareto optimizer 1236 for future or predicted time periods. In someembodiments, the advisory mode outputs 1240 include various predictedinfection risks and energy costs for different values of minimumventilation setpoint and supply temperature setpoint (e.g., differentPareto optimal solutions as described in greater detail above withreference to FIGS. 13-16). In some embodiments, the Pareto optimalsolutions or operating points are presented as suggested operatingpoints for a future time period.

In some embodiments, the analysis mode outputs 1234 (e.g., analysisresults over a previous or historical time period) and the advisory modeoutputs 1240 (e.g., suggested operating points for the HVAC system 300such as different Pareto optimal points), are determined (e.g.,detected, sensed, read from a meter, determined based on operatingparameters of equipment of the HVAC system 300, calculated, etc.)simultaneously and presented to the user simultaneously. In this way,the controller 1110 can both “look backwards” and “look forwards” toanalyze or assess previous operation of the HVAC system 300 and presentanalysis data, and to simultaneously determine suggested or simulatedsetpoints for future operation that minimize energy consumption orenergy cost (e.g., a Pareto optimal solution that has lowest energyconsumption or energy cost), minimize infection risk (e.g., a Paretooptimal solution that has lowest infection risk or highestdisinfection), or an equal priority operating point between minimizinginfection risk and minimizing energy consumption or energy cost,according to some embodiments.

In some embodiments, the previous or historical time period over whichdata is analyzed to determine the analysis mode outputs 1234 is adifferent length or time duration than the future time period for theadvisory mode outputs 1240. For example, the previous or historical timeperiod and the future time period can have different periodicities orthe same periodicities. In one example, the previous or historical timeperiod may be a previous 24 hours, while the future time period is a 1hour time horizon, a 12 hour time horizon, etc. In some embodiments, theperiodicities of the historical or previous time period and the futuretime period is user-selectable and can be adjusted by the user providinginputs to the controller 1110 via the display device 422. In someembodiments, the analysis mode outputs 1234 are for an hourly previoustime period and the advisory mode outputs 1240 are for a future 24 hourperiod. In some embodiments, the analysis mode outputs 1234 includecalculations of clean-air delivery and infection risk (e.g., based onBMS data obtained over the previous time period) such as minimumventilation setpoint, supply temperature setpoint, infection risk, andenergy cost. In some embodiments, the analysis mode outputs 1234 aredetermined based on sensor data and/or setpoints or operating parametersof the HVAC system 300 or equipment thereof (e.g., the AHU 304). In someembodiments, both the analysis mode outputs 1234 and the advisory modeoutputs 1240 are determined based on common models, configurations, anddata streams (e.g., the same data model 1202, the same modeling data1218, the same dynamic model simulator 1232, etc., except usinghistorical or previous data, and predicted or future data).

Analysis Mode Process

Referring particularly to FIG. 18, a process 1800 for determininganalysis mode outputs is shown, according to some embodiments. Process1800 can be performed for a previous or historical time period of thebuilding 10 using BMS data obtained over the previous or historical timeperiod, according to some embodiments. In some embodiments, process 1800is performed by the controller 1110. In some embodiments, process 1800includes steps 1802-1812 and can be performed simultaneously withprocess 1900 as described in greater detail below with reference to FIG.19.

Process 1800 includes obtaining one or more input parameters of one ormore zones of a building served by an HVAC system (step 1802), accordingto some embodiments. In some embodiments, the one or more inputparameters are timeseries values of the input parameters obtained (e.g.,via obtaining BMS data) over a previous or historical time period. Insome embodiments, step 1802 includes obtaining values of setpoints ofthe equipment of the HVAC system (e.g., the HVAC system 300) over theprevious or historical time period. In some embodiments, the values ofsetpoints include values of the minimum ventilation setpoint and/orsupply temperature setpoint (e.g., values of decision variables). Insome embodiments, the one or more input parameters include setpoints fortemperature, humidity, etc., of the building 10 or various zonesthereof. In some embodiments, step 1802 is performed the model generator1210 and/or the timeseries resampler 1212. In some embodiments, the oneor more input parameters are or include values of different infectionparameters such as a number of infected individuals, a number ofsusceptible individuals, a number of infectious individuals, avolumetric breath rate of one individual, a disease quanta generationrate, etc.

Process 1800 includes generating an infection model for the one or morezones of the building served by the HVAC system based on the one or moreinput parameters (step 1804), according to some embodiments. In someembodiments, the infection model predicts a probability of infection asa function of at least one of the one or more input parameters. In someembodiments, the infection model is a Wells-Riley based model. In someembodiments, step 1804 is performed by the controller 1110, or moreparticularly, by the model manager 416 using any of the techniquesdescribed in greater detail above with reference to the model manager416 (see e.g., FIG. 4).

Process 1800 includes obtaining an occupancy profile for the one or morezones of the building (step 1806), according to some embodiments. Insome embodiments, the occupancy profile includes a scheduled occupancyof each zone for the previous time period. In some embodiments, theoccupancy profile is timeseries data indicating a number of occupants ineach of the zones. In some embodiments, the occupancy profile isobtained from a scheduling service or from occupancy detectors (e.g.,detectors at the door that read a number of occupants that enter thebuilding 10 or that enter a specific zone). In some embodiments, step1806 is performed by the controller 1110 or more specifically by themodel manager 416. In some embodiments, the occupancy profile isgenerated based on zone scheduling and ASHRAE 90.1 standards.

Process 1800 includes performing a simulation of the infection model forthe previous time period (step 1808), according to some embodiments. Insome embodiments, the simulation is performed using the infection modelgenerated in step 1804. In some embodiments, the simulation is performedfor the previous time period using the one or more input parameters asobtained in step 1802. The simulation can be performed to determineinfection risks, infection probability, disinfection magnitude, etc.,resulting from the operation of the HVAC system over the previous timeperiod, according to some embodiments. In some embodiments, step 1808 isperformed by the optimization manager 412 or the dynamic model simulator1232. In some embodiments, the simulation is performed for a 24 hourperiod preceding a current time in 15 minute timesteps.

Process 1800 includes determining one or more infection metrics based onoutputs of the simulation (step 1810), according to some embodiments. Insome embodiments, the one or more infection metrics include infectionprobability, infection probability reduction, disinfection amount, etc.,of the zones of the building that is served by the HVAC system. In someembodiments, the infection metrics include ventilation rate of air forthe zones, clean-air delivery rate to the zones, infection risk, and/orclean air score. In some embodiments, step 1810 is performed by thedynamic model simulator 1232, the analysis mode outputs 1234, or theresults manager 418.

Process 1800 includes operating a display to provide the infectionmetrics of the previous time period to a user as analysis data (step1812), according to some embodiments. In some embodiments, step 1812 isperformed using the display device 422. In some embodiments, step 1812includes operating the display device 422 to provide any of theventilation rate of air for each of the zones, clean-air delivery rateto each of the zones, infection risk of each of the zones or of theoverall building, and/or clean air score for each of the zones. In someembodiments, the infection metrics are for the previous time period.

Advisory Mode Process

Referring particularly to FIG. 19, a process 1900 for determiningadvisory mode outputs is shown, according to some embodiments. Process1900 can be performed for a future or subsequent time period of thebuilding 10, according to some embodiments. In some embodiments, process1900 is performed simultaneously or concurrently with process 1800 sothat the future time period is relative to a current time, and theprevious or historical time period is also relative to the current time.Process 1900 can include steps 1902-1914 and can be performed by thecontroller 1110, according to some embodiments.

Process 1900 includes obtaining one or more input parameters of one ormore zones of a building served by an HVAC system (step 1902), accordingto some embodiments. In some embodiments, step 1902 is similar to step1802 as described in greater detail above with reference to FIG. 18 butis performed for a future time period. In some embodiments, step 1902includes defining one or more input parameters for use and obtaining BMSdata. In some embodiments, step 1902 is performed using the data model1202 and the modeling data 1218. In some embodiments, step 1902 isperformed by the timeseries resampler 1212.

Process 1900 includes performing a regression technique usingoperational data to determine key model parameters (step 1904),according to some embodiments. In some embodiments, step 1904 includesusing artificial intelligence, machine learning, a neural network, etc.,to train, adjust, calibrate, etc., different model parameters (e.g.,parameters of an infection risk model). In some embodiments, step 1904is performed using a predefined model or predefined model parameters(e.g., generic parameters) that is/are adjusted based on operationaldata obtained from the BMS of the HVAC system to improve an accuracy ofsimulations or predictions using the model.

Process 1900 includes generating an infection model for the one or morezones of the building served by the HVAC system based on the one or moreinput parameters (step 1906), according to some embodiments. In someembodiments, step 1906 is the same as or similar to step 1804 of process1800. In some embodiments, step 1906 is performed using the modelparameters that are updated, adjusted, calibrated, determined, etc., instep 1904 using the regression technique and operational data (e.g.,actual data of the HVAC system obtained from a BMS).

Process 1900 includes obtaining an occupancy profile for the one or morezones of the building (step 1908), according to some embodiments. Insome embodiments, step 1908 is the same as or similar to step 1806 ofprocess 1800 but is performed for a future time period. In someembodiments, step 1908 includes generating the occupancy profile for thezones based on ASHRAE standards and zone scheduling.

Process 1900 includes performing a simulation of the infection model fora future time period (step 1910), according to some embodiments. In someembodiments, step 1910 is the same as or similar to step 1808 of process1800 but performed for the future time period (e.g., a future timehorizon). In some embodiments, the simulation performed in step 1910 isperformed at a different periodicity (e.g., the duration of the futuretime period, and the time steps of the simulation performed at step 1910are different than the duration of the previous time period and the timesteps of the simulation performed at step 1808 of process 1800). In someembodiments, the simulation is performed to determine energy consumptionor energy cost and corresponding infection risks for different decisionvariables (e.g., minimum ventilation setpoint, supply temperaturesetpoint, etc.).

Process 1900 includes determining one or more infection metrics based onoutputs of the simulation (step 1912) and performing a Paretooptimization to determine different Pareto optimal operating points(step 1914), according to some embodiments. In some embodiments, step1912 is the same as or similar to the step 1810 of process 1800. In someembodiments, step 1914 includes performing steps 1706-1710 of process1700 as described in greater detail above with reference to FIG. 17. Forexample, the simulation performed in step 1910 can result in differentcombinations of energy cost or energy consumption and infection risk fordifferent operating parameters (e.g., for different values of decisionvariables). The Pareto optimization is performed to determine differentPareto optimal points that may be provided in step 1916 as suggestedoperating points or as advised operating points, according to someembodiments. In some embodiments, step 1914 includes determining whichof the Pareto optimal operating points result in lowest energy cost orenergy consumption, lowest infection risk (e.g., highest disinfection),and an equal priority between energy cost or energy consumption andinfection risk.

Process 1900 includes operating a display to provide the Pareto optimalpoints (or a subset thereof) to a user as advisory data (step 1916),according to some embodiments. In some embodiments, step 1916 includesproviding the Pareto optimal points associated with lowest or minimalenergy cost or energy consumption, lowest or minimal infection risk(e.g., maximum disinfection), and an equal priority Pareto optimal pointbetween energy consumption or cost and infection risk. In someembodiments, the Pareto optimal points are provided as advisory orsuggested operating conditions for the future time period.

Combined Analysis and Advisory Process

Referring particularly to FIG. 20 a process 2000 for performing both aninfection metric analysis for a previous time period and a Paretooptimization for a future time period is shown, according to someembodiments. In some embodiments, process 2000 includes steps 2002-2010and is performed by the controller 1110. In some embodiments, process2000 illustrates the simultaneous performance of process 1800 andprocess 1900.

Process 2000 includes performing an infection risk and energy costanalysis of an HVAC system for a previous time period to determineanalysis data (step 2002) and performing an infection risk and energycost Pareto optimization of the HVAC system for a future time period todetermine advisory data (step 2004), according to some embodiments. Insome embodiments, performing step 2002 includes performing process 1800.In some embodiments, performing step 2004 includes performing process1900. In some embodiments, steps 2002 and 2004 are performed at leastpartially simultaneously with each other.

Process 2000 includes operating a display to provide both the analysisdata and the advisory data to a user (step 2006), according to someembodiments. In some embodiments, step 2006 includes performing steps1812 and 1916 of processes 1800 and 1900, respectively. In someembodiments, step 2006 is performed by the display device 422. Providingboth the analysis data and the advisory data can facilitate a temporalbi-directional informing of the user regarding past operation of theHVAC system (e.g., the HVAC system 300) and suggested future suggestionsor advisory control decisions to achieve desired energy costs andinfection reduction or acceptable infection risk levels.

Process 2000 includes automatically selecting control decisions orreceiving a user input of a selected control decision (step 2008) andoperating equipment of an HVAC system according to the control decisions(step 2010), according to some embodiments. In some embodiments, steps2008 and 2010 are the same as or similar to steps 1714 and 1716 ofprocess 1700.

User Interfaces

Referring particularly to FIGS. 21-23, different user interfaces 2100,2200, and 2300 display the various outputs of the controller 1110 (e.g.,the display data), according to some embodiments. In some embodiments,the user interface 2100, 2200, and 2300 are displayed on the displaydevice 422 and presented to a user or a building administrator. The userinterface 2100 shows display of the analysis mode outputs 1234, the userinterface 2200 shows display of the advisory mode outputs 1240, and theuser interface 2300 shows checklists for implementing one of the variousoptions of the advisory mode outputs 1240.

Referring particularly to FIG. 21, the user interface 2100 includes aninfectious disease risk score icon 2102, and an indoor air quality scoreicon 2104. In some embodiments, the infectious disease risk score 2102is a scaled version of the infection risk for the previous time period.In some embodiments, the infectious disease risk score is a weightedaverage, a time-series average, etc., of the infection risks of zones ofthe building 10 over the previous time period. In some embodiments, theindoor air quality score icon 2104 displays a similarly aggregated,average, etc., score of the indoor air quality of the zones of thebuilding 10 over the previous time period. In some embodiments, thevalues of the infectious disease risk score and the indoor air qualityscore are normalized values from ranging from 0 or 1 to 100. In someembodiments, the indoor air quality score icon 1204 and the infectiousdisease risk score icon 2102 are graphical icons that display a bar or acircle chart and a textual or numeric value of the indoor air qualityscore and the infectious disease risk score for the zones of thebuilding 10 over the previous time period. In some embodiments, theindoor air quality score icon 1204 and the infectious disease risk scoreicon 2102 are color-coded based on their values. For example, if theindoor air quality score is between a first or normal range, then thecolor of the indoor air quality score icon 1204 may be yellow, accordingto some embodiments. In some embodiments, if the indoor air qualityscore is between a second range or less than a lower value of the firstor normal range, this may indicate that the indoor air quality score ispoor and the color of the indoor air quality score icon 2104 may be red.In some embodiments, if the indoor air quality score is between a thirdrange or greater than a higher value of the first or normal range, thismay indicate that the indoor air quality score is good and the color ofthe indoor air quality score 2104 may be green.

Referring still to FIG. 21, the user interface 2100 includes a list 2106of one or more infectious disease high risk alerts, according to someembodiments. In some embodiments, the list 2106 includes different items2108, each item corresponding to a different zone of the building 10 andan individual infection risk score associated with the different zones.In some embodiments, the items 2108 of the list 2106 are zone-specificand are determined based on the infectious disease risk score for eachof the zones of the building 10. For example, if one of the zones has anassociated infectious disease risk score that is below a thresholdamount, then that zone may be added with the associated infectiousdisease risk score to the list 2106 as one of the items 2108.

Referring still to FIG. 21, the user interface 2100 also includes a list2110 of one or more low indoor air quality alerts, according to someembodiments. In some embodiments, the list 2110 includes different items2112, each item corresponding to a different zone of the building 10 andan individual indoor air quality associated with the different zones. Insome embodiments, the items 2112 of the list 2110 are zone-specific andare determined based on the indoor air quality for each of the zones ofthe building 10. For example, if one of the zones has an associatedindoor air quality that is below a threshold amount, then that zone maybe added with the associated indoor air quality to the list 2110 as oneof the items 2112.

Referring still to FIG. 21, the user interface 2100 includes a list 2114of each of the zones of the building 10 (e.g., organized by zone type,floor of the building 10, etc.). Each of the items of the list 2114includes an indication of the zone or floor, an associated infectiousdisease risk score for the zone or floor, a number of infectious diseaserisk alerts for the zone or floor, an indoor air quality score for thezone or floor, an indoor air quality trend (e.g., a 30 day trend), anumber of indoor air quality alerts, and/or an energy spend versusbudget (e.g., for 30 days).

Referring to FIG. 22, the user interface 2200 includes different widgets2202-2208 indicating the results of the Pareto optimization (e.g., theadvisory mode outputs 1240) as described in greater detail above withreference to FIGS. 11-20. Specifically, the user interface 2200 includesa current operational state widget 2202 illustrating current energycosts and associated infectious disease risk score with additional airflow, comfort, UV disinfection, and filtration specifics, according tosome embodiments. The user interface 2200 includes a widget 2204illustrating a first option, namely, the Pareto optimal result foroptimizing the infectious disease risk score (e.g., minimizing infectionrisk or infection probability such as the maximum disinfection point1318), a widget 2206 illustrating a second option, namely, the Paretooptimal result for equal priority between disinfection and energyconsumption (e.g., the equal priority point 1320), and a widget 2208illustrating a third option, namely, the Pareto optimal result foroperating with minimum energy cost (e.g., the minimum energy consumptionpoint 1322). Each of the widgets 2204-2208 include graphical and/ortextual information regarding a corresponding infectious disease riskscore, an energy cost per a time period (e.g., a monthly time period),air flow parameters, required operational adjustments, optional designadjustments, etc., for each of the options. In some embodiments, theuser or building administrator may select one of the options byselecting one of the widgets 2204-2208.

Referring particularly to FIG. 23, the user interface 2300 illustratesdifferent operational adjustments for the HVAC system 400 that thebuilding administrator should implement in order to configure the HVACsystem 400 to perform the selected option, according to someembodiments. The user interface 2300 includes widgets 2302a-2302d, eachof which illustrate a next step that should be performed to implementthe selected option, according to some embodiments. In some embodiments,each widget 2302 includes a button 2304 which, when selected, navigatesthe user to a command and control panel where the user or buildingadministrator can perform the specific operational adjustment (e.g.,adjusting the supply temperature setpoint). Each widget 2302 alsoincludes a button 2306 which, when selected, marks the task associatedwith the widget 2302 as completed, according to some embodiments.

Sustainability Metric Techniques

Referring to FIGS. 24-30, various techniques for performing the Paretooptimization based on a sustainability metric are shown, according tosome embodiments. In some embodiments, the sustainability metric can beintroduced into the Pareto optimization as a third control objectivesuch that the Pareto optimization considers energy cost, infection risk,and the sustainability metric. In some embodiments, the sustainabilitymetric may replace one of the control objectives discussed above (e.g.,replacing energy cost or infection risk) such that the Paretooptimization considers energy cost and the sustainability metric (asshown in FIGS. 26 and 30) or considers infection risk and thesustainability metric (as shown in FIG. 24).

The sustainability metric may include any of a variety of metrics thatquantify the performance of a building, campus, or organization withrespect to energy sustainability or environmental sustainability. Someexamples of sustainability metrics include carbon dioxide (CO2) relatedmetrics (i.e., carbon equivalents) such as carbon emissions, carbonfootprint, carbon credits, carbon offsets, and the like. Other examplesof sustainability metrics include greenhouse gas emissions (e.g.,methane, nitrous oxide, fluorinated gases, etc.), water usage, waterpollution, waste generation, ecological footprint, resource consumption,or any other metric that can be used to quantify sustainable buildingoperations. In some embodiments, sustainability metrics can be expressedon a per unit basis such as carbon per number of widgets produced,carbon per volume of product produced, carbon per meals served, carbonper patients treated, carbon per experiments run, carbon per salesrevenue, carbon per items shipped, carbon per emails sent, carbon perunit of data processed, carbon per occupant, carbon per occupied room,carbon per normalized utilization value, etc. In some embodiments,sustainability metrics can be generated on an enterprise-wide basis(e.g., one value for the whole enterprise), on a building-by-buildingbasis, on a campus-by-campus basis, by business unit/department, bybuilding system or subsystem (e.g., HVAC, lighting, security, etc.), bycontrol loop (e.g., chiller control loop, AHU control loop, watersidecontrol loop, airside control loop, etc.), by building space (e.g., perroom or floor,) or by any other division or aggregation. Sustainabilitymetrics can be calculated or generated based on actual or historicalbuilding operations or predicted for future building operations usingone or more predictive models.

The techniques described herein with reference to FIGS. 24-27 can beperformed or implemented by the controller 1110, the functionality ofthe controller 1110 as shown in the diagram 1200, etc., with the one ormore sustainability metrics used in the Pareto optimization as anadditional parameter (e.g., an additional degree of freedom for theoptimization to thereby result in points that define a Pareto optimalsurface), in place of the energy cost or consumption, in place ofinfection risk, or as a post-processing calculation to determine asustainability metric or carbon equivalence for the various proposedsolutions or operating schedules. Advantageously, the sustainabilitytechniques described herein can be used for at least one of (i) anoperational optimization to minimize or to inform a buildingadministrator regarding sustainable building operation, or (ii) a designoptimization to determine infrastructure (e.g., building equipment, HVACequipment, etc.) that results in a cost-effective and sustainable (e.g.,reduced carbon emissions) HVAC system infrastructure.

It should be understood that the sustainability metric described hereinprovides an estimation of how sustainable or environmentally friendly aproposed solution is (e.g., in terms of carbon emissions). Therefore,“high” or “maximum” values of the sustainability metric indicate anincreased amount of carbon emissions and decreased or minimalenvironmentally friendliness of the solution, and “low” values of thesustainability metric indicate a decreased amount of carbon emissionsand increased or maximal environmentally friendliness of the solution.It should further be understood that while FIGS. 24-29 described hereinshow infection risk being used as one of the optimization objectives(e.g., one of the parameters that is calculated by an objectivefunction), the optimization objectives can also be a combination of thesustainability metric and an energy consumption or energy cost (e.g., asshown in FIG. 30).

Referring particularly to FIG. 24, a diagram 2400 shows the graph 1302of different decision variables (e.g., supply temperature setpoint andminimum ventilation setpoint), and a graph 2404 that shows correspondingobjective function values, shown as points 2408, for each of thedifferent combinations of decision variables. The decision variables1306 as shown in the graph 1302 of FIG. 24 may be the same as thedecision variables 1306 as shown in the graph 1302 of FIG. 13 or anyother decision variables that can be adjusted to influence the objectivefunction values. In the embodiment shown in FIG. 24, the objectivefunction values are infection risk and a sustainability metric. In otherembodiments, the objective function values may be the sustainabilitymetric and energy cost (described in greater detail with reference toFIG. 30). It is contemplated that any set of objective function valuescan be used and the teachings of the present disclosure are not limitedto the specific examples provided herein. The sustainability metric canbe an estimated amount of CO2 emissions that are predicted to occur dueto operation according to the minimum ventilation setpoint and supplytemperature setpoint, or any other sustainability metric as described indetail above.

The objective function and corresponding predictive models used todefine the sustainability metric and the infection risk can be similarto the objective function and predictive models described above withreference to FIGS. 11-20, with the exception that the sustainabilitymetric is calculated/predicted in place of energy cost orconsumption(e.g., as shown in the graph 2404). For each combination ofthe decision variables 1306 (i.e., for each of the points 1306 a-1306l), the controller 1110 may perform a simulation to determinecorresponding values 2408 a-2408 l of the control objectives, asdescribed in greater detail above with reference to FIGS. 13-15 andFIGS. 17-20. In this way, the steps of the Pareto optimization asdescribed in greater detail above with reference to FIGS. 13-15 can beperformed (e.g., by the controller 1110) using an objective functionthat predicts a sustainability metric and an infection risk.

In some embodiments, the value of the sustainability metric iscalculated or predicted directly using one or more predictive modelsthat define a relationship between the sustainability metric andbuilding control decisions. For example, a predictive model may definethe amount of carbon emissions as a function of operating decisions forbuilding equipment (e.g., equipment on/off decisions, operatingsetpoints, etc.) over the duration of the optimization period. In otherembodiments, the value of the sustainability metric can be calculatedbased on a corresponding amount of energy consumption. In this scenario,the objective function may be the same as the objective functionpreviously described (e.g., an objective function that predicts energycost or energy consumption as a function of the supply temperaturesetpoint and the minimum ventilation setpoint), and the resulting valueof the objective function (e.g., energy consumption or cost) can beconverted to a value of the sustainability metric (e.g., the carbonequivalence) using a conversion relationship. In some embodiments, theconversion relationship is a linear relationship that is used to mapenergy cost or energy consumption (e.g., for the HVAC system 200) tocarbon emissions equivalence or any other sustainability metric.

Referring particularly to FIG. 25, a graph 2500 shows a relationshipbetween energy cost and carbon equivalence for an operationalimplementation of the Pareto optimization, according to someembodiments. The graph 2500 includes points 2504 and a trendline 2502that represents the relationship between the energy cost and the carbonequivalent. In some embodiments, the trendline 2502 is a linearrelationship (e.g., y=mx+b) that can be used to convert between energycost and carbon equivalent in either direction (e.g., to estimate anenergy cost based on carbon emissions, or to estimate carbon emissionsor carbon equivalent based on energy cost). In some embodiments, therelationship shown in FIG. 25 is used to convert an output of theobjective function from energy consumption to the carbon equivalentprior to performing the Pareto optimization described in greater detailabove with reference to FIGS. 13-15, in process 1700, process 1900, etc.In some embodiments, the relationship shown in FIG. 25 is used when thecontroller 1110 is implemented in an on-line mode for an operationaloptimization.

Referring particularly to FIG. 26, a graph 2600 shows a relationshipbetween total cost (e.g., a sum of capital expenses for purchase andinstallation of equipment, and energy cost associated with operating theequipment) and carbon equivalent is shown, according to someembodiments. In some embodiments, the relationship shown in FIG. 26 isused for an off-line implementation of the controller 1110 (e.g., whenthe functionality of the controller is implemented as a design tool orused to determine what equipment should be purchased). The graph 2600includes points 2604 and a curve fit 2602 that illustrates therelationship between the total cost and the carbon equivalent (e.g., acurve fit approximation of the points 2604). In some embodiments, therelationship between total cost and the carbon equivalent is used by thecontroller 1110 when the capital cost is affected by a decision variableor depends on a decision variable (e.g., when the controller 1110 isused to determine what equipment should be purchased or used, or toprovide a recommendation to a building administrator regarding whatequipment should be purchased). In some embodiments, the relationship asshown in FIG. 26 illustrates that as the carbon equivalent increases, asignificant tradeoff between carbon emissions and total cost may occur(e.g., the total cost may be significantly reduced but causeincreasingly higher carbon equivalents).

Referring to FIG. 27, the diagram 1200 that illustrates thefunctionality of the controller 1110 (see e.g., FIG. 12, above) is shownas diagram 2700, modified to account for sustainability instead ofenergy cost or energy consumption, according to some embodiments. Insome embodiments, the components of the diagram 2700 are the same as thecomponents of the diagram 1200 but with an additional sustainabilityconversion 2702 that is performed either (i) using an output of thedynamic model simulator 1232 to convert the resulting objective functionvalues into a sustainability metric (e.g., CO2 emission or carbonequivalent), (ii) using an output of the Pareto optimizer 1236 toconvert the optimized values to a sustainability metric (e.g., CO2emission or carbon equivalent) so that at least one of the optimizedvalues in terms of energy cost or energy consumption or the carbonequivalent is provided to the user as the advisory mode outputs 1240 orthe analysis mode outputs 1234, or (iii) using a different generic modelsimulation 1230 that predicts the sustainability metric as a function ofone or more decision variables, or incorporates a conversion betweenenergy consumption or cost and the sustainability metric.

As shown in FIG. 27, the sustainability conversion 2702 can beimplemented using an output of the dynamic model simulator 1232 toconvert the objective function values from being in terms of energy costor energy consumption to being in terms of the sustainability metric. Insome embodiments, the sustainability conversion 2702 is configured toreceive values of the objective function from the dynamic modelsimulator 1232 (e.g., values of energy cost or energy consumption) anddetermine a corresponding or equivalent value of a sustainability metricsuch as carbon or CO2 emissions. In some embodiments, the sustainabilityconversion 2702 or any of the other sustainability conversions describedherein is/are implemented using the linear relationship shown in FIG. 25or using the curve-fit relationship as shown in FIG. 26. In someembodiments, the linear relationship shown in FIG. 25 is implementedwhen the controller 1110 operates to perform operational optimizations,and the curve-fit relationship as shown in FIG. 26 is implemented whenthe controller 1110 operates to perform building design and operationaloptimization. In some embodiments, the sustainability conversion 2702 isimplemented using outputs of the Pareto optimizer 1236, or as part of apost-process when providing the analysis mode outputs 1224 or theadvisory mode outputs 1240 to the user.

Referring still FIGS. 27, 4-5, and 11, the functionality of thesustainability conversion 2702 can be performed in an on-demand mannerin response to a user input, according to some embodiments. In someembodiments, the user can provide an input to the controller 1110 totransition use of the sustainability conversion 2702 or to toggle thecontroller 1110 from operating using an objective function that predictsenergy consumption or energy cost, and an objective function thatpredicts the sustainability metric. In this way, the dynamic modelsimulator 1232 can be transitioned between performing a simulation forenergy consumption or energy cost (e.g., the objective function values)and performing a simulation for a sustainability metric. In someembodiments, the functionality of the sustainability conversion 2702 isperformed as a display feature. For example, the Pareto optimal valuesmay be provided to the user (e.g., via the display device 422, a userinterface, a display screen, etc.) in terms of energy consumption orenergy cost, and can be toggled (e.g., in response to a user input) tothe sustainability metric (e.g., using the linear relationship shown inFIG. 25) in response to a user input. In this way, the user can useeither energy consumption, energy cost, or the sustainability metric todetermine which control decisions to select. In some embodiments, thecontroller 1110 operates to provide both the sustainability metric andthe energy cost or consumption to the user (e.g., via the display device422) without requiring a user input.

Referring to FIGS. 13 and 24, all of the infection risk, the energy costor consumption, and the sustainability metric can be used to determineobjective function values based on one or more decision variables,according to some embodiments. Specifically, while FIGS. 13 and 24 showonly two objective function values (e.g., predicted energycost/consumption and predicted infection risk in FIG. 13, and predictedsustainability metric and predicted infection risk in FIG. 24), theobjective function values may be combined so that more than twoobjective function values are used to assess Pareto optimality of thedifferent combinations of decision variables. In some embodiments, thesustainability metric, the energy cost or consumption, and the infectionrisk are calculated using several different objective functions todetermine a surface of points (e.g., each point having a value of thesustainability metric, the infection risk, and the energy cost orconsumption). The subsequent steps of determining feasible points, andthe various Pareto optimal points can be performed by the controller1110 similarly as described above but using the surface graph. In someembodiments, the equal priority point is an equal priority between thesustainability metric, the infection risk, and the energy cost orconsumption, and may be an inflection point of the surface of feasiblepoints that is identified by the controller 1110.

Referring particularly to FIG. 28, a process 2800 shows the process 1700modified to use the sustainability metric in place of the energy cost orenergy consumption, according to some embodiments. In some embodiments,the process 2800 is the same as the process 1700 but includes anadditional step 2802 performed using the outputs of the simulationperformed in step 1704. Process 2800 includes converting values of theenergy cost and infection risk to values of a sustainability metric andinfection risk (step 2802), according to some embodiments. In someembodiments, step 2802 includes using either of the relationships shownin FIGS. 25 and 26 to convert the energy cost or energy consumptionresulting from the simulations into a corresponding value of carbonemissions (e.g., the sustainability metric).

Process 2800 also includes modified steps 2804, 2806, and 2808, andsteps 1712-1716 of process 1700, according to some embodiments. In someembodiments, the modified step 2804 is the same as the step 1706 but isperformed based on the sustainability metric instead of the energy cost.Similarly, step 2806 can be the same as or similar to the step 1708 butperformed to determine Pareto optimal solutions based on thesustainability metric. Finally, step 2808 can be the same as the step1710 of the process 1700 but performed to determined various of thePareto optimal points (e.g., a minimum sustainability metric solution, amaximum disinfection solution, and an equal prioritysustainability/disinfection solution), according to some embodiments. Insome embodiments, the step 2802 is incorporated in the step 1704, or thesimulation is performed to determine sets of values of thesustainability metric and the infection risk directly. In such animplementation, step 2802 can be performed to determine energy cost orenergy consumption based on the determined values of the sustainabilitymetric.

Referring particularly to FIG. 29, a process 2900 for performing aPareto optimization while accounting for the sustainability metric of anHVAC system, the energy cost, and an infection risk is shown, accordingto some embodiments. Process 2900 includes steps 2902-2916 and can bethe same as or similar to the steps 1702-1716 of process 1700. Process2900 differs from the process 1700 in that the process 2900 is performedfor three objective function values (the energy cost, the sustainabilitymetric, and the infection risk) instead of only two objective functionvalues (the energy cost and the infection risk).

Particularly, process 2900 includes performing a simulation for each setof the values of the control decision variables to determine sets ofvalues of energy cost, a sustainability metric, and infection risk (step2904), according to some embodiments. In some embodiments, step 2904 isperformed by the controller 1110 similarly to step 1704 but for severalobjective function values (e.g., optimization objectives). In someembodiments, step 2904 is performed using multiple objective functions,namely, an objective function that estimates energy cost based on thecontrol decision variables, an objective function that estimates asustainability metric based on the control decision variables, and anobjective function that estimates or predicts infection risk based onthe control decision variables. In some embodiments, the objectivefunction used to predict the sustainability metric is the same as theobjective function used to predict the energy cost but with anadditional conversion factor or function to convert the energy cost tothe sustainability metric.

Process 2900 includes determining which of the sets of values of energycost, the sustainability metric, and the infection risk are infeasibleand which are feasible (step 2906), according to some embodiments. Insome embodiments, the sets of values of energy cost, sustainabilitymetric, and the infection risk are used to construct a surface or 3-dplot. In some embodiments, the step 2906 includes comparing variousvalues of the control decision variables, or values of any of the energycost, the sustainability metric, or the infection risk to constraints(e.g., user-specified constraints, system operating constraints, etc.)to determine which of the sets of values of the energy cost, thesustainability metric, or the infection risk are feasible or infeasible.

Process 2900 includes determining which of the feasible sets of valuesof energy cost, the sustainability metric, and the infection risk arePareto optimal solutions (step 2908), according to some embodiments. Insome embodiments, step 2908 is performed similarly to step 1708 ofprocess 1700 but also accounting for the sustainability metric. In someembodiments, the Pareto optimal solutions are curves that definemultiple Pareto optimal solutions. Process 2900 includes determining,based on the Pareto optimal solutions, a minimum energy cost solution, amaximum disinfection solution, a minimum sustainability metric solution,and an equal priority solution (step 2910), according to someembodiments. In some embodiments, step 2910 is similar to step 1710 butalso accounts for the sustainability metric. In some embodiments, thePareto optimal solutions are curves that define multiple Pareto optimalsolutions along the surface graph in terms of the minimum energy costsolution, the maximum disinfection solution, the minimum sustainabilitymetric solution, and the equal priority solution. In some embodiments,the equal priority solution is an equal priority between the energycost, the infection risk, and the sustainability metric.

Process 2900 includes steps 2912-2916 that are the same as or similar tosteps 1712-1716 but also including display and accordingly userselection of options that take into account the sustainability metric.In some embodiments, only one of the sustainability metric or the energycost is displayed to the user via the display screen, and the user maytoggle between the sustainability metric and the energy cost for thedifferent proposed solutions to facilitate proper selection.

Referring to FIG. 30, another diagram 3000 shows a graph 3002 ofdifferent decision variables, and a graph 3004 of correspondingobjective function values for each of the different decision variables.The graph 3002 can be the same as or similar to the graph 1302 asdescribed in greater detail above with reference to FIG. 13. As shown inFIG. 30, the graph 3002 shows different combinations for a firstdecision variable (the Y-axis) and a second decision variable (theX-axis) for the HVAC system 300, illustrated as points 3006, accordingto some embodiments. In some embodiments, the first decision variableand the second decision variable are minimum temperature setpoint andminimum ventilation setpoint for the HVAC system 300. It should beunderstood that the decision variables 3006 are not limited to theminimum temperature setpoint and the minimum ventilation setpoint andmay be any other setpoints, operating parameters, etc., such astemperature setpoints, humidity setpoints, comfort parameters, HVACoperating parameters, etc. The points 3006 are shown to include points3006 a-3006 l, each point corresponding to a different pair of objectivefunction values.

In some embodiments, a simulation is performed using one or more dynamicmodels to determine one or more corresponding values of Paretooptimization objectives (e.g., values of the sustainability metric andthe energy cost) for each of the decision variables, represented by thepoints 3006. In some embodiments, the corresponding values of the Paretooptimization objectives are shown as points 3008, including points 3008a-3008 l. Each of the points 3008 a-3008 l correspond to one of thepoints 3006 a-3006 l. In some embodiments, the one or more dynamicmodels include models that predict energy cost and/or the sustainabilitymetric as a function of both the first decision variable and the seconddecision variable. In some embodiments, the points 3008 are determinedby the dynamic model simulator 1232 based on the different values of thefirst decision variable and the second decision variable using one ormore dynamic models.

The points 3008 can be used by the Pareto optimizer 1236 or the Paretooptimizer 1112 to determine which of the points 3008 are feasible andin-feasible, and to further determine which of the feasible points 3008are Pareto optimal points in terms of sustainability (e.g., a Paretooptimal point having a lowest value of the sustainability metric),energy cost (e.g., a Pareto optimal point having a lowest value ofenergy cost), or an equal priority Pareto point that optimizes both thesustainability metric and the energy cost equally, according to someembodiments. In some embodiments, the sustainability metric accounts foroperational carbon emissions (e.g., if the Pareto optimization isperformed in the context of an operational tool) or accounts for carbonemissions resulting from both operation of the HVAC system 300 and/orinstalling equipment in the HVAC system 300 (e.g., if the Paretooptimization is performed in the context of a design tool). In someembodiments, the points 3008 are used for selection or determination ofthe various Pareto optimal points. These Pareto optimal points may beautomatically selected for use by the HVAC system 300 or may bepresented to a building administrator for selection thereof. Each of thePareto optimal points corresponds to different values of the decisionvariables or schedules of decision variables over a time period (e.g.,setpoints over a future time period) and selection of one of the Paretooptimal points of the points 3008 results in the selection of thecorresponding decision variables or schedules of the decision variables.

Once a particular Pareto optimal point of the Pareto optimal points 3008are selected, the controller 1110 or the controller 310 generatescontrol signals for the HVAC system 300 to operate the HVAC system 300according to the selected Pareto optimal point (e.g., according to thecorresponding combination of decision variables or the correspondingschedule of the decision variables over a time horizon such as a futuretime horizon).

Configuration of Exemplary Embodiments

Although the figures show a specific order of method steps, the order ofthe steps may differ from what is depicted. Also two or more steps canbe performed concurrently or with partial concurrence. Such variationwill depend on the software and hardware systems chosen and on designerchoice. All such variations are within the scope of the disclosure.Likewise, software implementations could be accomplished with standardprogramming techniques with rule based logic and other logic toaccomplish the various connection steps, calculation steps, processingsteps, comparison steps, and decision steps.

The construction and arrangement of the systems and methods as shown inthe various exemplary embodiments are illustrative only. Although only afew embodiments have been described in detail in this disclosure, manymodifications are possible (e.g., variations in sizes, dimensions,structures, shapes and proportions of the various elements, values ofparameters, mounting arrangements, use of materials, colors,orientations, etc.). For example, the position of elements can bereversed or otherwise varied and the nature or number of discreteelements or positions can be altered or varied. Accordingly, all suchmodifications are intended to be included within the scope of thepresent disclosure. The order or sequence of any process or method stepscan be varied or re-sequenced according to alternative embodiments.Other substitutions, modifications, changes, and omissions can be madein the design, operating conditions and arrangement of the exemplaryembodiments without departing from the scope of the present disclosure.

As used herein, the term “circuit” may include hardware structured toexecute the functions described herein. In some embodiments, eachrespective “circuit” may include machine-readable media for configuringthe hardware to execute the functions described herein. The circuit maybe embodied as one or more circuitry components including, but notlimited to, processing circuitry, network interfaces, peripheraldevices, input devices, output devices, sensors, etc. In someembodiments, a circuit may take the form of one or more analog circuits,electronic circuits (e.g., integrated circuits (IC), discrete circuits,system on a chip (SOCs) circuits, etc.), telecommunication circuits,hybrid circuits, and any other type of “circuit.” In this regard, the“circuit” may include any type of component for accomplishing orfacilitating achievement of the operations described herein. Forexample, a circuit as described herein may include one or moretransistors, logic gates (e.g., NAND, AND, NOR, OR, XOR, NOT, XNOR,etc.), resistors, multiplexers, registers, capacitors, inductors,diodes, wiring, and so on).

The “circuit” may also include one or more processors communicablycoupled to one or more memory or memory devices. In this regard, the oneor more processors may execute instructions stored in the memory or mayexecute instructions otherwise accessible to the one or more processors.In some embodiments, the one or more processors may be embodied invarious ways. The one or more processors may be constructed in a mannersufficient to perform at least the operations described herein. In someembodiments, the one or more processors may be shared by multiplecircuits (e.g., circuit A and circuit B may comprise or otherwise sharethe same processor which, in some example embodiments, may executeinstructions stored, or otherwise accessed, via different areas ofmemory). Alternatively or additionally, the one or more processors maybe structured to perform or otherwise execute certain operationsindependent of one or more co-processors. In other example embodiments,two or more processors may be coupled via a bus to enable independent,parallel, pipelined, or multi-threaded instruction execution. Eachprocessor may be implemented as one or more general-purpose processors,application specific integrated circuits (ASICs), field programmablegate arrays (FPGAs), digital signal processors (DSPs), or other suitableelectronic data processing components structured to execute instructionsprovided by memory. The one or more processors may take the form of asingle core processor, multi-core processor (e.g., a dual coreprocessor, triple core processor, quad core processor, etc.),microprocessor, etc. In some embodiments, the one or more processors maybe external to the apparatus, for example the one or more processors maybe a remote processor (e.g., a cloud based processor). Alternatively oradditionally, the one or more processors may be internal and/or local tothe apparatus. In this regard, a given circuit or components thereof maybe disposed locally (e.g., as part of a local server, a local computingsystem, etc.) or remotely (e.g., as part of a remote server such as acloud based server). To that end, a “circuit” as described herein mayinclude components that are distributed across one or more locations.

The present disclosure contemplates methods, systems and programproducts on any machine-readable media for accomplishing variousoperations. The embodiments of the present disclosure can be implementedusing existing computer processors, or by a special purpose computerprocessor for an appropriate system, incorporated for this or anotherpurpose, or by a hardwired system. Embodiments within the scope of thepresent disclosure include program products comprising machine-readablemedia for carrying or having machine-executable instructions or datastructures stored thereon. Such machine-readable media can be anyavailable media that can be accessed by a general purpose or specialpurpose computer or other machine with a processor. By way of example,such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROMor other optical disk storage, magnetic disk storage or other magneticstorage devices, or any other medium which can be used to carry or storedesired program code in the form of machine-executable instructions ordata structures and which can be accessed by a general purpose orspecial purpose computer or other machine with a processor. Combinationsof the above are also included within the scope of machine-readablemedia. Machine-executable instructions include, for example,instructions and data which cause a general purpose computer, specialpurpose computer, or special purpose processing machines to perform acertain function or group of functions.

What is claimed is:
 1. A controller for heating, ventilation, or airconditioning (HVAC) equipment operable to affect an environmentalcondition of a building, the controller comprising: one or moreprocessors; and memory storing instructions that, when executed by theone or more processors, cause the one or more processors to performoperations comprising: obtaining one or more predictive modelsconfigured to predict values of a carbon emissions control objective andanother control objective as a function of control decision variablesfor the HVAC equipment; executing an optimization process using the oneor more predictive models to produce multiple sets of optimizationresults corresponding to different values of the control decisionvariables, the carbon emissions control objective, and the other controlobjective; selecting one or more of the sets of optimization resultsbased on the values of the carbon emissions control objective and theother control objective; and operating the HVAC equipment to affect theenvironmental condition of the building in accordance with the values ofthe control decision variables corresponding to a selected set of theoptimization results.
 2. The controller of claim 1, wherein the carbonemissions control objective comprises an amount of carbon emissionspredicted to result from operating the HVAC equipment in accordance withthe control decision variables.
 3. The controller of claim 1, whereinthe other control objective comprises an infection risk predicted toresult from operating the HVAC equipment in accordance with the controldecision variables.
 4. The controller of claim 1, wherein the othercontrol objective comprises at least one of an operating cost predictedto result from operating the HVAC equipment in accordance with thecontrol decision variables or a capital cost of purchasing or installingthe HVAC equipment.
 5. The controller of claim 1, wherein executing theoptimization process comprises executing multiple optimization processesusing different sets of constraints for the control decision variablesor different search spaces for the control decision variables, themultiple optimization processes producing corresponding sets of themultiple sets of optimization results.
 6. The controller of claim 1,wherein selecting one or more of the sets of optimization resultscomprises selecting one or more of the sets of optimization results forwhich the values of the carbon emissions control objective and the othercontrol objective are not both improved by another of the sets ofoptimization results
 7. The controller of claim 1, wherein selecting oneor more of the sets of optimization results comprises: classifying themultiple sets of optimization results as either Pareto-optimaloptimization results or non-Pareto-optimal optimization results withrespect to the carbon emissions control objective and the other controlobjective; and selecting the Pareto-optimal optimization results.
 8. Thecontroller of claim 1, wherein selecting one or more of the sets ofoptimization results comprises selecting: a first set of optimizationresults that prioritizes the carbon emissions control objective over theother control objective; a second set of optimization results thatprioritizes the other control objective over the carbon emissionscontrol objective; and a third set of optimization results that balancesthe carbon emissions control objective and the other control objective.9. The controller of claim 8, the operations further comprising:presenting the values of the carbon emissions control objective and theother control objective associated with the first set of optimizationresults, the second set of optimization results, and the third set ofoptimization results as selectable options via a user interface; anddetermining the selected set of the optimization results responsive to auser selecting one of the selectable options via the user interface. 10.A controller for heating, ventilation, or air conditioning (HVAC)equipment operable to affect an environmental condition of a building,the controller comprising: one or more processors; and memory storinginstructions that, when executed by the one or more processors, causethe one or more processors to perform operations comprising: obtainingone or more predictive models configured to predict values of asustainability control objective and another control objective as afunction of control decision variables for the HVAC equipment; executingan optimization process using the one or more predictive models toproduce multiple sets of optimization results corresponding to differentvalues of the control decision variables, the sustainability controlobjective, and the other control objective; selecting one or more of thesets of optimization results for which the values of the sustainabilitycontrol objective and the other control objective are not both improvedby another of the sets of optimization results; and operating the HVACequipment to affect the environmental condition of the building inaccordance with the values of the control decision variablescorresponding to a selected set of the optimization results.
 11. Thecontroller of claim 10, wherein the sustainability control objectivecomprises an amount of carbon emissions predicted to result fromoperating the HVAC equipment in accordance with the control decisionvariables.
 12. The controller of claim 10, wherein the other controlobjective comprises an infection risk predicted to result from operatingthe HVAC equipment in accordance with the control decision variables.13. The controller of claim 10, wherein the other control objectivecomprises at least one of an operating cost predicted to result fromoperating the HVAC equipment in accordance with the control decisionvariables or a capital cost of purchasing or installing the HVACequipment.
 14. The controller of claim 10, wherein executing theoptimization process comprises executing multiple optimization processesusing different sets of constraints for the control decision variablesor different search spaces for the control decision variables, themultiple optimization processes producing corresponding sets of themultiple sets of optimization results.
 15. The controller of claim 10,wherein selecting one or more of the sets of optimization resultscomprises: classifying the multiple sets of optimization results aseither Pareto-optimal optimization results or non-Pareto-optimaloptimization results with respect to the sustainability controlobjective and the other control objective; and selecting thePareto-optimal optimization results.
 16. The controller of claim 10,wherein selecting one or more of the sets of optimization resultscomprises selecting: a first set of optimization results thatprioritizes the sustainability control objective over the other controlobjective; a second set of optimization results that prioritizes theother control objective over the sustainability control objective; and athird set of optimization results that balances the sustainabilitycontrol objective and the other control objective.
 17. The controller ofclaim 16, the operations further comprising: presenting the values ofthe sustainability control objective and the other control objectiveassociated with the first set of optimization results, the second set ofoptimization results, and the third set of optimization results asselectable options via a user interface; and determining the selectedset of the optimization results responsive to a user selecting one ofthe selectable options via the user interface.
 18. A controller for aheating, ventilation, or air conditioning (HVAC) system for a building,the controller comprising: one or more processors; and memory storinginstructions that, when executed by the one or more processors, causethe one or more processors to perform operations comprising: obtainingone or more predictive models configured to predict values of asustainability control objective and another control objective as afunction of control decision variables for the HVAC equipment; executinga Pareto optimization process using the one or more predictive models toproduce one or more sets of Pareto optimal values of the controldecision variables, the sustainability control objective, and the othercontrol objective; and operating the HVAC equipment to affect theenvironmental condition of the building in accordance with a selectedset of the Pareto optimal values of the control decision variables. 19.The controller of claim 18, wherein executing the Pareto optimizationprocess comprises: executing multiple optimization processes to producecorresponding sets of optimization results comprising values of thecontrol decision variables, the sustainability control objective, andthe other control objective; and selecting, as the one or more sets ofPareto optimal values, one or more of the sets of optimization resultsfor which the values of the sustainability control objective and theother control objective are not both improved by another of the sets ofoptimization results.
 20. The controller of claim 18, wherein: thesustainability control objective comprises an amount of carbon emissionspredicted to result from operating the HVAC equipment in accordance withthe control decision variables; and the other control objectivecomprises at least one of: an infection risk predicted to result fromoperating the HVAC equipment in accordance with the control decisionvariables; an operating cost predicted to result from operating the HVACequipment in accordance with the control decision variables; or acapital cost of purchasing or installing the HVAC equipment.